| Sample Questions |
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| Title :
AE
Try This
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| Q:
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'(A+B)(A2-AB+B2)' |
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Show Answer
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Using The Identity,
(X+Y)(X2 - XY + Y2) = X3 + X3
Here X=A, Y=B
= A3 + B3
= A3+B3
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| Title :
AE
Try This
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| Q:
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'(2X+3Y+4Z)2' |
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Show Answer
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Using The Identity,
(A + B + C)2 = A2 + B2 + C2 + 2AB + 2BC + 2CA
Here A = 2X, B = 3Y, C = 4Z
= 2X2 + 3Y2 + 4Z2 + 2(2X)(3Y) + 2(3Y)(4Z) + 2(4Z)(2X)
= 4X2+9Y2+16Z2+12XY+24YZ+16XZ
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| Title :
AE
Try This
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| Q:
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'(3Y-2X)3' |
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Show Answer
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Using The Identity,
(A - B)3 = A3 - B3 - 3AB(A - B)
Here A=3Y, B=2X
= 3Y3 - 2X3 - 3(3Y)(2X)((3Y) - (2X))
= 27Y3-8X3 - 18XY(3Y - 2X)
= 27Y3-8X3+36X2Y-54XY2
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| Title :
AE
Try This
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| Q:
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'102 * 106' |
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Show Answer
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Using, The Identity (X+A)(X+B) = X2 + (A+B)X + AB
Here X = 100, A = 2 and B = 6
102 × 106 = (100 + 2)(100 + 6)
= 1002 + (2 + 6)100 + 2 × 6
= 10000 + 800 + 12
= 10812
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| Title :
AE
Try This
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| Q:
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'12^3' |
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Show Answer
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Using, The Identity (A+B)3 = A3 + B3 +3AB(A+B)
Here A = 10 and B = 2
123 = (10 + 2)3
= 103 + 23 +3 × 10 × 2 (10 + 2)
= 1000 + 8 + 60(12)
= 1000 + 8 + 720
= 1728
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| Title :
AE
Try This
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| Q:
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'34^2 - 32^2' |
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Show Answer
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Using, The Indentity A2 - B2 = (A-B)(A+B)
Here A = 34 and B = 32
Here 342 - 322 = (34-32)(34+32)
= (2)(66)
= 132
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| Title :
AE
Try This
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'9^3' |
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Show Answer
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Using, The Identity (A-B)3 = A3 - B3 -3AB(A-B)
Here A = 10 and B = 1
93 = (10 - 1)3
= 103 - 13 -3 × 10 × 1 (10 - 1)
= 1000 - 1 - 30(9)
= 1000 - 1 - 270
= 729
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| Title :
AE
Try This
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| Q:
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'10^3 - 7^3 - 3^3' |
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Show Answer
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Here A = 10, B = -7, C = -3
Therefore, A+B+C = (10) + (-7) + (-3) = 0
If A + B + C = 0 then A3 + B3 + C3 = 3ABC
103 + -73 + -33 = 3(10)(-7)(-3) = 630
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| Title :
AE
Try This
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| Q:
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'4^3 + 3^3' |
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Show Answer
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Using, The Indentity A3 + B3 = (A+B)(A2-AB+B2)
Here A = 4 and B = 3
43 + 33 = (4 + 3)(A2 - 4 × 3 + B2)
= (7)(16 - 12 + 9)
= 7 * 13
= 91
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