December 22, 2007

Arithmetic: Division of Decimal Numbers

ProblemDividendDivisorQuotient
18.488233.36130.0364
2169.60460.4605368.3053
30.04963.07110.0162
40.09450.45050.2098
50.846319.24230.044
698.41930.07631289.8991
77.15813.10312.3068
80.56020.031118.0129
9347.30410.6389543.597
106.20960.348517.8181
110.1343591.67280.0002
1214.7355877.1470.0168
137.97450.654512.1841
148.09540.161350.1885
1558.48310.05191126.842
1678.36360.02083767.4808
170.0016866.71040
180.25180.001251.8
193.04911.38072.2084
2056.26878.05286.9875
21634.413215.773640.2199
224.2809539.45630.0079
23438.76653.5674122.9934
245.581862.86570.0888
250.087710.49030.0084
264.21810.05379.5868
270.08720.01098
280.408815.82020.0258
290.05390.00153.9
300.30151.27590.2363
31194.90156.050732.2114
320.085319.15570.0045
33621.8137318.31011.9535
345.89540.068486.1901
350.048.20630.0049
361.12751.57340.7166
372.85750.035580.493
3887.68610.05631557.4796
3989.688293.49430.9593
403.2360.43427.4528
410.054353.74710.001
4290.1243411.05710.2193
43542.157145.992811.7879
440.00940.00990.9495
458.30360.471617.6073
460.173867.74280.0026
472.6699895.31950.003
481.6401760.02470.0022
490.02020.66540.0304
501.452681.06380.0179

Arithmetic: Multiplication of Decimal Numbers

ProblemMultiplicandMultiplierProduct
10.2092196.58841.1262096
20.79230.94660.74999118
36.25941.23147.70782516
40.02260.05260.00118876
50.0433.88150.1669045
6980.49630.056855.69218984
70.00930.03520.00032736
824.57490.02720.66843728
945.53261.98082822.1097856
10346.447633.26411524.2329664
110.17710.84610.14984431
120.0012.20090.0022009
1395.83180.05675.43366306
140.450870.235231.66202816
150.026454.90121.44939168
160.0667583.211238.90018704
179.21830.01980.18252234
180.03270.29420.00962034
190.741525.801719.13196055
2089.57140.00920.82405688
215.86830.00720.04225176
222.25850.68951.55723575
230.073645.40247.114346
2425.94549.5754248.43758316
251.3689791.19891083.07217421
2638.38820.08853.3973557
270.68870.76720.52837064
280.05143.90180.20055252
290.08782.05670.18057826
304.4258509.99772257.14782066
310.77250.92850.71726625
328.9806265.83592387.36588354
333.9820.02480.0987536
341.93070.89181.72179826
3513.10740.25433.33321182
36127.692695.785712231.12507582
378.48080.04190.35534552
3857.7499.3628540.6923372
390.00955.40410.05133895
4058.2553131.26817647.06254593
410.76370.03030.02314011
42443.44420.025811.44086036
430.00910.01010.00009191
447.00799.574667.09783934
459.5315300.03062859.7416639
460.032779.14542.58805458
470.06960.03270.00227592
48576.14080.9258533.39115264
490.87588.70657.6251527
500.7122887.541632.1067002

Arithmetic: Subtraction of Decimal Numbers

ProblemMinuendSubtrahendDifference
10.0540.04930.0047
216.16080.938115.2227
3428.979371.1015357.8778
4632.288524.5929607.6956
56.57120.0076.5642
66.75140.06896.6825
7418.36750.0096418.3579
830.324315.907614.4167
9992.35123.5296988.8216
1065.07956.415958.6636
11786.9899136.2085650.7814
12160.10770.6419159.4658
137.13120.00957.1217
14204.09170.6831203.4086
151.56370.01141.5523
16955.76430.7823954.982
1757.74410.012957.7312
189.40480.80928.5956
191.33030.06971.2606
2080.79025.541475.2488
210.02740.00090.0265
22981.97020.0565981.9137
2352.26020.037652.2226
24189.92460.0584189.8662
2547.17310.62846.5451
260.29050.03070.2598
27996.62770.6105996.0172
280.08640.08210.0043
290.79370.00090.7928
300.31470.07530.2394
311.4050.08071.3243
327.24640.95746.289
330.78980.7880.0018
340.05720.00940.0478
350.76960.08660.683
36743.67160.0272743.6444
370.06020.04640.0138
38684.2305580.3356103.8949
39213.19190.0974213.0945
408.52130.0018.5203
41945.79930.3815945.4178
4280.56460.343780.2209
4327.21511.49525.7201
44153.72227.1016146.6206
455.6740.41635.2577
4611.46040.490310.9701
472.19440.50411.6903
480.00940.0010.0084
493.7990.08773.7113
5027.28870.0627.2287

Arithmetic: Addition of Decimal Numbers

ProblemFirst NumberSecond NumberTotal
18.9623297.7417306.704
2701.393456.8087758.2021
30.08030.03750.1178
40.26050.39880.6593
592.2453200.2868292.5321
69.10420.08489.189
755.38750.04655.4335
80.80274.3755.1777
90.251892.234792.4865
100.125614.246614.3722
110.25970.06290.3226
120.00174.88364.8853
1394.9920.973495.9654
1470.03810.844770.8828
15830.4316591.16171421.5933
16375.1138897.61981272.7336
170.0325635.6434635.6759
180.21362.90633.1199
1994.7286247.4069342.1355
2018.61660.009518.6261
213.6850.06983.7548
220.09230.07450.1668
231.03550.53471.5702
240.9847515.7856516.7703
256.61017.919714.5298
260.0092332.66332.6692
273.10290.07663.1795
280.57224.79955.3717
297.2010.57597.7769
30296.149489.8571386.0065
310.50850.26550.774
3295.667192.5247188.1918
330.0210.06780.0888
343.01098.383411.3943
3519.50220.061519.5637
360.04856.27226.3207
3782.45370.60283.0557
380.57494.11114.686
390.2779564.1305564.4084
400.88310.03920.9223
410.62838.06488.6931
420.074830.232330.3071
430.4190.73891.1579
446.429643.4785649.9075
4560.9713267.7551328.7264
4691.7453278.0438369.7891
470.17980.80980.9896
485.77926.454332.2333
490.00240.05120.0536
509.8455356.8249366.6704

Arithmetic: Division of Integers

ProblemDividendDivisorQuotient
19101091
26275711
37501550
47041164
59903033
65201052
79361852
84701047
97707710
107285613
111301310
124514111
131701017
143481229
151901019
161240226477
178768897904
186878076905
191386014990
201185771167
217781298794
221781347379
233925943913
243678253694
251303218724
262389426919
275526060921
286279078805
293029454561
305444883656
312421122
323421819
335461342
341901910
356403220
367801078
374642916
384291139
397261166
408334917
417773721
429409410
438701087
443001225
458253325
464029692438
474841291532
482831038745
491478219778
503576048745

Arithmetic: Multiplication of Integers

ProblemMultiplicandMultiplierProduct
16905940710
27528060160
34945527170
43994116359
59652726055
64343716058
76984833504
85895130039
93979738509
101798915931
111776711859
128534639238
139636865484
144877837986
154066526390
16764826631064
17172873150156
18782221172822
19616420258720
2027923164449
21950616585200
22606527319362
23782179139978
2430033199300
25867439380613
26939793744627
27337500168500
28183899164517
29230782179860
30352705248160
319599591105
324706530550
339042522600
344919044190
356758557375
362843610224
374053313365
384987336354
398824943218
406052716335
412687018760
424507935550
437138157753
445113316863
455844224528
46849291247059
47766595455770
48529725383525
49377896337792
50527633333591

Arithmetic: Subtraction of Integers

ProblemMinuendSubtrahendDifference
178188693
234022683134
334009762424
472447677
5321517
659006635237
743349
829003732527
9421824
1016025881014
11842856
1229276216
1380437767
1467589
1524019421459
16655510
1759397496
18964749
1913419115
2085832
211003576427
2224001332267
2366597
2474677
2572182639
2653025074795
271276760
2854006824718
2923001912109
3020005791421
3189054298476
3270002576743
3344727420
3443057753530
3518001931607
3637559316
3793001469154
3899199892
3917548127
4067055186187
4170747660
42511635
43743737
44731756
4586818850
4698016489153
47422517
4831068772229
4926197
5084117824

Arithmetic: Addition of Integers

ProblemFirst NumberSecond NumberSum
1340489829
2372293665
33748541228
42298071036
5598104702
66189501568
7171541712
89272981225
99042641168
10168293461
11360440800
123047721076
138257681593
149275251452
156099621571
166037441347
17100638738
184568811337
194517041155
20577212789
212429071149
229243061230
23714118832
24647130777
25315100415
266676751342
276343961030
282659711236
291999761175
306315311162
3168066746
3296813981
3313972211
34977841061
3546396559
3680012812
3771284796
3884088928
3967617693
4087138909
4177781858
4241778495
43976891065
4422045265
4569067757
4682146867
4715271223
4820797304
49912951007
5053165596

Arithmetic: Division of Fractions

ProblemDividendDivisorQuotient
17/815/1614/15
24/213/148/9
31/185/217/30
47/81/87
57/163/101 11/24
67/181/155 5/6
75/221/204 6/11
87/243/141 13/36
97/127/121
107/201/144 9/10
112/37/816/21
122/155/1812/25
135/144/151 19/56
141/185/147/45
153/222/211 19/44
163/227/1218/77
171/181/181
188/93/205 25/27
191/153/102/9
207/243/222 5/36
217/81/1815 3/4
224/217/1824/49
237/157/161 1/15
245/87/85/7
251/107/126/35
267/163/162 1/3
278/211/228 8/21
287/97/88/9
295/217/1050/147
307/125/242 4/5
317/245/127/10
324/910/2114/15
338/93/205 25/27
341/121/201 2/3
358/97/91 1/7
365/127/221 13/42
377/107/101
386/78/927/28
395/241/142 11/12
407/121/158 3/4
415/165/211 5/16
425/147/1845/49
437/94/71 13/36
441/223/2010/33
457/201/248 2/5
464/211/203 17/21
477/202/213 27/40
487/245/1614/15
498/95/91 3/5
501/141/241 5/7

Multiplication of Fractions

ProblemMultiplicandMultiplierProduct
12/74/98/63
21/165/215/336
35/75/1425/98
45/245/2425/576
55/94/920/81
65/165/1825/288
77/127/1249/144
81/187/127/216
91/141/121/168
108/153/104/25
118/95/1820/81
123/227/1021/220
138/91/98/81
148/151/241/45
157/157/2249/330
167/127/1849/216
177/83/521/40
187/104/1514/75
191/241/101/240
201/157/247/360
214/218/2132/441
225/163/1615/256
236/79/2027/70
241/217/181/54
251/244/151/90
267/247/2049/480
277/203/2021/400
285/161/125/192
291/228/154/165
301/181/211/378
311/107/187/180
323/105/181/12
331/241/161/384
341/127/207/240
351/165/225/352
367/247/1649/384
373/221/223/484
387/107/1849/180
392/32/34/9
403/53/49/20
411/47/47/16
427/128/1514/45
433/207/247/160
445/147/201/8
457/201/227/440
467/245/1235/288
471/187/107/180
484/55/182/9
491/147/121/24
504/157/207/75

Arithmetic: Subtraction of Fractions

ProblemMinuendSubtrahendDifference
11/127/12-1/2
25/121/1813/36
37/227/10-21/55
41/165/18-31/144
55/127/241/8
65/127/2213/132
75/227/16-37/176
86/75/813/56
91/242/15-11/120
108/91/16119/144
111/228/15-161/330
125/83/81/4
133/145/12-17/84
147/227/10-21/55
153/54/5-1/5
165/215/12-5/28
175/181/108/45
185/217/22-37/462
194/211/1817/126
203/201/151/12
217/121/2115/28
228/153/1683/240
233/161/1413/112
242/38/9-2/9
251/121/141/84
263/201/1411/140
275/128/15-7/60
283/511/12-19/60
293/141/1211/84
303/55/2447/120
317/181/1420/63
323/143/163/112
334/95/2417/72
348/211/1413/42
356/73/73/7
362/31/127/12
377/103/2011/20
385/127/181/36
398/910/2126/63
405/75/910/63
411/165/14-33/112
427/247/18-7/72
435/183/144/63
442/217/10-127/210
455/227/12-47/132
467/183/2043/180
477/207/16-7/80
481/203/20-1/10
493/143/140
505/241/1517/120

Arithmetic: Addition of Fractions

ProblemFirst NumberSecond NumberTotal
15/243/1061/120
21/213/1411/42
34/91/2297/198
45/127/2417/24
51/201/2221/220
65/128/2167/84
71/105/2437/120
85/165/1475/112
96/74/91 19/63
107/207/1214/15
112/97/91
127/181/1022/45
133/167/15157/240
143/221/2222/121
155/141/1237/84
167/165/21227/336
175/141/2117/42
187/151/1211/20
191/222/1559/330
201/21/21
217/205/21247/420
221/247/1561/120
233/143/2227/77
241/107/2223/55
258/91/2467/72
268/921/221 167/198
275/144/15131/210
288/217/1227/28
297/103/101
304/72/534/35
317/101/1834/45
324/153/22133/330
331/78/91 2/63
347/101/104/5
357/101/203/4
362/310/211 1/7
377/185/182/3
381/33/1019/30
397/167/18119/144
402/214/1538/105
417/167/101 11/80
426/78/91 47/63
433/41/41
445/221/1241/132
455/165/2425/48
465/95/14115/126
473/227/1046/55
485/161/163/8
491/155/2132/105
501/155/1489/210

Analytic Geometry: Equation and Slope of a Line

Given two points each for line P1P2 and line AB, the equations and slopes of the lines are determined. Through their slopes,

it's determined whether the lines are parallel or perpendicular to each other.

ProblemGiven PointsEquations of the LineSlopes of the Line
1P1(-4,5) P2(0,3); A(7,11) B(11,9)x+2y-6=0, x+2y-29=0parallel lines: m1=-1/2 m2=-1/2
2P1(-3,1) P2(1,5); A(4,12) B(2,10)x-y+4=0, x-y+8=0parallel lines: m1=1/1 m2=1/1
3P1(6,5) P2(4,3); A(4,4) B(2,6)x-y-1=0, x+y-8=0perpendicular lines: m1=1/1 m2=1/-1
4P1(6,1) P2(8,4); A(3,3) B(6,1)3x-2y-16=0, 2x+3y-15=0perpendicular lines: m1=3/2 m2=-2/3
5P1(9,7) P2(5,0); A(0,6) B(7,2)7x-4y-35=0, 4x+7y-42=0perpendicular lines: m1=-7/-4 m2=-4/7
6P1(-3,8) P2(7,2); A(9,10) B(14,7)3x+5y-31=0, 3x+5y-77=0parallel lines: m1=-3/5 m2=-3/5
7P1(4,5) P2(8,1); A(5,1) B(9,5)x+y-9=0, x-y-4=0perpendicular lines: m1=-1/1 m2=1/1
8P1(-2,0) P2(4,8); A(14,14) B(8,6)4x-3y+8=0, 4x-3y-14=0parallel lines: m1=4/3 m2=-4/-3
9P1(7,3) P2(4,5); A(7,4) B(9,7)2x+3y-23=0, 3x-2y-13=0perpendicular lines: m1=2/-3 m2=3/2
10P1(4,3) P2(5,8); A(2,1) B(7,0)5x-y-17=0, x+5y-7=0perpendicular lines: m1=5/1 m2=-1/5
11P1(-4,1) P2(0,5); A(2,3) B(5,6)x-y+5=0, x-y+1=0parallel lines: m1=1/1 m2=1/1
12P1(-1,0) P2(9,3); A(14,3) B(4,0)3x-10y+3=0, 3x-10y-12=0parallel lines: m1=3/10 m2=-3/-10
13P1(-2,9) P2(6,7); A(12,3) B(8,4)x+4y-34=0, x+4y-24=0parallel lines: m1=-1/4 m2=1/-4
14P1(7,7) P2(6,9); A(7,7) B(9,8)2x+y-21=0, x-2y+7=0perpendicular lines: m1=2/-1 m2=1/2
15P1(-1,4) P2(8,9); A(2,8) B(11,13)5x-9y+41=0, 5x-9y+62=0parallel lines: m1=5/9 m2=5/9
16P1(7,8) P2(3,4); A(8,1) B(4,5)x-y+1=0, x+y-9=0perpendicular lines: m1=1/1 m2=1/-1
17P1(-6,9) P2(3,6); A(6,8) B(0,10)x+3y-21=0, x+3y-30=0parallel lines: m1=-1/3 m2=1/-3
18P1(-8,2) P2(4,5); A(8,1) B(4,0)x-4y+16=0, x-4y-4=0parallel lines: m1=1/4 m2=-1/-4
19P1(3,9) P2(7,7); A(3,0) B(5,4)x+2y-21=0, 2x-y-6=0perpendicular lines: m1=-1/2 m2=2/1
20P1(6,7) P2(0,0); A(7,0) B(0,6)7x-6y+0=0, 6x+7y-42=0perpendicular lines: m1=-7/-6 m2=6/-7

Analytic Geometry: Equation of a Line

Given two points, the equation of a line whose points are equidistant from the two given points is determined.
ProblemGiven PointsEquation of the Line
1P1(-3,5) P2(-2,-5)2x-20y+5=0
2P1(9,7) P2(1,-1)1x+1y-8=0
3P1(3,7) P2(-9,-4)24x+22y+39=0
4P1(4,8) P2(-1,5)5x+3y-27=0
5P1(9,-6) P2(-4,-9)13x+3y-10=0
6P1(-8,7) P2(7,-5)10x-8y+13=0
7P1(3,4) P2(-6,-8)6x+8y+25=0
8P1(4,-3) P2(-8,-4)24x+2y+55=0
9P1(1,8) P2(3,-9)4x-34y-25=0
10P1(-1,3) P2(8,-7)18x-20y-103=0
11P1(-3,4) P2(-8,-4)10x+16y+55=0
12P1(9,1) P2(-9,6)36x-10y+35=0
13P1(-5,9) P2(-8,-3)2x+8y-11=0
14P1(-2,2) P2(3,-1)5x-3y-1=0
15P1(2,1) P2(2,-4)0x-2y-3=0
16P1(8,7) P2(-3,-9)22x+32y-23=0
17P1(5,-3) P2(-8,-8)13x+5y+47=0
18P1(7,1) P2(-5,5)3x-1y-0=0
19P1(-9,1) P2(3,-5)2x-1y+4=0
20P1(1,3) P2(8,-1)14x-8y-55=0
21P1(3,-5) P2(-4,-9)14x+8y+63=0
22P1(-3,6) P2(-6,-6)2x+8y+9=0
23P1(5,7) P2(-5,-7)5x+7y-0=0
24P1(4,9) P2(-9,1)26x+16y-15=0
25P1(4,1) P2(-5,-4)9x+5y+12=0
26P1(5,6) P2(-3,9)16x-6y+29=0
27P1(-8,4) P2(-4,-7)8x-22y+15=0
28P1(-1,3) P2(4,-2)1x-1y-1=0
29P1(3,5) P2(6,-1)2x-4y-1=0
30P1(6,-2) P2(-7,-3)13x+1y+9=0

Analytic Geometry: Distance Between Two Points

Given two points, their distance and the slope of the line joining them are solved.
ProblemGiven PointsDistanceSlope
1P1(2,4) P2(7,8)sqrt of 414/5
2P1(8,6) P2(4,7)sqrt of 171/-4
3P1(1,-3) P2(-3,-6)sqrt of 25-3/-4
4P1(-6,7) P2(5,-6)sqrt of 290-13/11
5P1(-1,5) P2(-8,-2)sqrt of 981/1
6P1(1,7) P2(9,-3)sqrt of 164-5/4
7P1(5,6) P2(-2,-7)sqrt of 218-13/-7
8P1(9,8) P2(4,9)sqrt of 261/-5
9P1(3,9) P2(-2,1)sqrt of 89-8/-5
10P1(4,1) P2(3,9)sqrt of 658/-1
11P1(6,3) P2(-8,4)sqrt of 1971/-14
12P1(7,6) P2(2,2)sqrt of 41-4/-5
13P1(4,-2) P2(-6,-9)sqrt of 149-7/-10
14P1(8,4) P2(2,2)sqrt of 40-1/-3
15P1(3,3) P2(8,-4)sqrt of 74-7/5
16P1(-2,8) P2(-1,-9)sqrt of 290-17/1
17P1(2,5) P2(7,9)sqrt of 414/5
18P1(3,8) P2(-4,-5)sqrt of 218-13/-7
19P1(6,4) P2(8,8)sqrt of 202/1
20P1(-4,3) P2(5,-6)sqrt of 162-1/1
21P1(-9,3) P2(-5,-8)sqrt of 137-11/4
22P1(4,3) P2(1,5)sqrt of 132/-3
23P1(4,-6) P2(-5,-7)sqrt of 82-1/-9
24P1(4,4) P2(1,-9)sqrt of 178-13/-3
25P1(-4,8) P2(8,-6)sqrt of 340-7/6
26P1(5,2) P2(1,9)sqrt of 657/-4
27P1(8,7) P2(-1,-4)sqrt of 202-11/-9
28P1(1,8) P2(9,3)sqrt of 89-5/8
29P1(1,9) P2(-6,5)sqrt of 65-4/-7
30P1(8,2) P2(2,8)sqrt of 721/-1
31P1(8,-3) P2(-2,-5)sqrt of 104-1/-5
32P1(3,3) P2(-4,-2)sqrt of 74-5/-7
33P1(8,8) P2(5,9)sqrt of 101/-3
34P1(8,3) P2(2,5)sqrt of 401/-3
35P1(9,6) P2(-6,4)sqrt of 229-2/-15
36P1(8,6) P2(1,-2)sqrt of 113-8/-7
37P1(5,3) P2(7,5)sqrt of 81/1
38P1(-8,8) P2(-3,-3)sqrt of 146-11/5
39P1(-4,7) P2(1,-9)sqrt of 281-16/5
40P1(7,9) P2(1,7)sqrt of 40-1/-3
41P1(-4,8) P2(-9,-3)sqrt of 146-11/-5
42P1(-3,3) P2(7,-7)sqrt of 200-1/1
43P1(8,2) P2(-7,7)sqrt of 2501/-3
44P1(2,1) P2(3,9)sqrt of 658/1
45P1(8,2) P2(4,9)sqrt of 657/-4
46P1(1,7) P2(8,8)sqrt of 501/7
47P1(3,-8) P2(-1,-4)sqrt of 321/-1
48P1(9,7) P2(1,4)sqrt of 73-3/-8
49P1(2,7) P2(5,-3)sqrt of 109-10/3
50P1(7,4) P2(-3,-8)sqrt of 244-6/-5

Algebra: Least Common Multiple (LCM)

Solution SetGiven NumbersLCM
15,13,10130
228,9,201260
310,15,330
422,12,172244
53,2,1212
68,10,21840
712,3,1648
810,8,11440
921,19,151995
1018,24,872
1117,16,12816
1219,17,206460
1319,18,12684
1417,15,181530
1522,2,7154
166,7,13546
1717,14,222618
1822,9,132574
1918,23,135382
2016,12,20240
2119,17,51615
223,5,1260
2318,14,24504
244,23,171564
2522,13,236578
2621,15,171785
2715,7,191995
2820,14,15420
297,14,642
3013,21,82184
3115,21,6210
3214,22,161232
3316,17,154080
349,6,218
3519,5,7665
367,12,20420
3724,6,424
3817,20,61020
3922,18,132574
4011,23,92277
4113,17,204420
4222,2,666
4313,4,9468
442,3,1818
453,20,460
463,21,642
4721,11,173927
4813,23,216279
4912,2,13156
5015,14,2210

Algebra: Greatest Common Divisor (GCD)

Solution SetGiven NumbersGCD
154,48,606
28,48,408
3598,322,71323
440,80,488
520,40,324
670,10,5010
787,493,66729
815,18,303
9195,91,6513
1042,48,126
1170,30,6010
128,10,142
13341,93,21731
1444,33,7711
1528,40,324
16620,155,34131
1728,40,244
18207,115,32223
19115,621,39123
2060,50,3010
2149,70,637
2242,18,546
2345,20,505
24290,377,49329
2535,25,55
2649,70,637
2748,72,3612
28266,475,55119
29403,155,43431
3049,28,567
3154,60,126
32667,87,63829
333,15,123
3484,36,7212
35459,51,28917
3632,8,488
3795,209,55119
3824,8,328
3927,6,153
40221,91,24713
41187,51,32317
4216,24,204
4311,66,3311
4463,56,287
4521,18,303
4663,18,819
4748,12,8412
4872,12,4812
4930,60,4010
5011,33,6611

Algebra: Linear Equations in Two Unknown

Given two linear equations, the two equations are solved simultaneously for x and y.
ProblemGiven EquationsSolution
17x+5y = 38; 6x+3y = 30x = 4; y = 2
24x+7y = 18; 6x+9y = 24x = 1; y = 2
3x+8y = 29; 6x+8y = 94x = 13; y = 2
46x+4y = -26; 3x+7y = -68x = 3; y = -11
59x+y = 101; x+9y = 29x = 11; y = 2
63x+7y = 51; 2x+9y = 60x = 3; y = 6
7x+4y = 47; 7x+4y = 89x = 7; y = 10
83x-3y = -72; x+9y = 96x = -12; y = 12
9x+2y = 33; x+4y = 61x = 5; y = 14
10x+8y = 78; 8x+y = 120x = 14; y = 8
115x+2y = 57; 5x+4y = 79x = 7; y = 11
12x+y = 20; 9x+y = 108x = 11; y = 9
135x+7y = 102; 8x+6y = 132x = 12; y = 6
145x+7y = 133; 8x+9y = 193x = 14; y = 9
157x+3y = 43; 3x+y = 15x = 1; y = 12
164x+3y = 43; 9x+4y = 61x = 1; y = 13
179x+8y = 150; 4x+y = 59x = 14; y = 3
189x+2y = 19; 7x+6y = -43x = 5; y = -13
195x+y = 24; 4x+7y = 106x = 2; y = 14
205x+9y = 83; 8x+2y = 46x = 4; y = 7
21x+4y = -44; 2x+8y = -88x = 8; y = -13
229x+9y = 216; 5x+4y = 107x = 11; y = 13
236x+y = 74; 5x+8y = 76x = 12; y = 2
243x+9y = 72; 4x+4y = 64x = 12; y = 4
254x+7y = -65; 2x+4y = -38x = 3; y = -11
265x+y = 62; 2x+y = 32x = 10; y = 12
274x+y = 18; 3x+2y = 21x = 3; y = 6
288x+5y = 18; 9x+2y = -16x = -4; y = 10
299x+9y = 216; 9x+6y = 174x = 10; y = 14
30x+4y = 17; 8x+5y = 82x = 9; y = 2
315x+2y = 24; 8x+y = 34x = 4; y = 2
329x+7y = 166; x+y = 20x = 13; y = 7
333x+7y = 104; 5x+9y = 144x = 9; y = 11
347x+7y = 0; 8x+8y = 0x = 4; y = -4
354x+7y = 94; 2x+7y = 68x = 13; y = 6
367x+2y = 34; 2x+3y = 34x = 2; y = 10
378x+8y = 104; 9x+9y = 117x = 2; y = 11
38x+9y = 128; 3x+3y = 72x = 11; y = 13
395x+8y = 22; 7x-9y = -50x = -2; y = 4
409x+6y = 54; 6x+9y = -24x = 14; y = -12
415x+4y = 65; 3x+9y = 105x = 5; y = 10
422x+9y = 56; 6x+5y = 36x = 1; y = 6
437x+6y = 59; 6x+6y = 54x = 5; y = 4
448x+5y = 85; 2x+7y = 73x = 5; y = 9
453x+8y = 41; 3x+2y = 35x = 11; y = 1
467x+y = 71; 7x+2y = 72x = 10; y = 1
475x+9y = 79; 2x+y = 16x = 5; y = 6
489x+8y = -93; 6x+2y = -72x = -13; y = 3
499x+y = 85; x+4y = 25x = 9; y = 4
509x+6y = 156; 8x+8y = 152x = 14; y = 5

Algebra: Multiplication of Polynomials



ProblemGiven PolynomialsSolution
12x+12 and 7x+914x2+102x+108
21x+13 and 7x-137x2+78x-169
38x-2 and 8x+564x2+24x-10
41x-12 and 5x-115x2-71x+132
51x-11 and 5y-115xy-11x-55y+121
65x4+7 and 1x2+85x6+40x4+7x2+56
75x+4 and 7x2-735x3-35x1+28x2-28
87x3-1 and 2y2+1214x3y2+84x3-2y2-12
96x-13 and 2y2-212xy2-12x-26y2+26
104x2-10 and 3y3-112x2y3-4x2-30y3+10
113x3+5y4 and 1x+2y3x4+6x3y+5xy4+10y5
122x2-2y4 and 4x2+3y38x4+6x2y3-8x2y4-6y7
131x+7y2 and 4x-1y34x2-1xy3+28xy2-7y5
141x2-3y2 and 5x3-1y5x5-1x2y-15x3y2+3y3
155x+2y3 and 3x315x4+6x3y3
164x2+5y4 and 2x8x3+10xy4
176x4-7y2 and 1x46x8-7x4y2
187x+13 and 4x+528x2+87x+65
197x+12 and 8x-1456x2-2x-168
203x-6 and 8x+124x2-45x-6
218x-9 and 5x-340x2-69x+27
223x-2 and 4y-312xy-9x-8y+6
235x4+12 and 6x2+830x6+40x4+72x2+96
248x+6 and 4x2-932x3-72x1+24x2-54
254x3-14 and 3y2+112x3y2+4x3-42y2-14
265x-3 and 4y2-1220xy2-60x-12y2+36
278x2-11 and 2y3-1416x2y3-112x2-22y3+154
284x2+3y4 and 6x4+5y324x6+20x2y3+18x4y4+15y7
295x4-6y2 and 2x+2y210x5+10x4y2-12xy2-12y4
302x2+6y and 8x3-3y216x5-6x2y2+48x3y-18y3
312x2-7y4 and 1x-1y2x3-2x2y-7xy4+7y5
322x4+1y4 and 1x2x5+1xy4
335x4+2y and 1x45x8+2x4y
344x4-2y3 and 1x34x7-2x3y3
354x+4 and 2x+28x2+16x+8
361x+10 and 8x-88x2+72x-80
378x-1 and 1x+148x2+111x-14
387x-12 and 5x-135x2-67x+12
396x-12 and 4y-1124xy-66x-48y+132
407x4+13 and 6x2+442x6+28x4+78x2+52
413x+3 and 7x2-221x3-6x1+21x2-6
424x3-1 and 7y2+728x3y2+28x3-7y2-7
433x-10 and 2y2-26xy2-6x-20y2+20
442x2-5 and 1y3-112x2y3-22x2-5y3+55
455x4+4y4 and 8x3+4y440x7+20x4y4+32x3y4+16y8
467x3-6y2 and 2x+1y214x4+7x3y2-12xy2-6y4
471x2+3y2 and 3x2-3y3x4-3x2y+9x2y2-9y3
485x2-4y and 8x4-2y440x6-10x2y4-32x4y+8y5
491x2+8y2 and 7x7x3+56xy2
502x4+6y3 and 2x44x8+12x4y3