Problem : 1 [ Algebraic Expression ]       Solve this type of problem 1. (A+B)(A2-AB+B2)   Show Answer A: Using The Identity, (X+Y)(X2 - XY + Y2) = X3 + X3 Here X=A, Y=B = A3 + B3 = A3+B3

Problem : 2 [ Algebraic Expression ]       Solve this type of problem 2. (2X+3Y+4Z)2   Show Answer A: 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

Problem : 3 [ Algebraic Expression ]       Solve this type of problem 3. (3Y-2X)3   Show Answer A: 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

Problem : 4 [ Algebraic Expression ]       Solve this type of problem 4. 102 * 106   Show Answer A: 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

Problem : 5 [ Algebraic Expression ]       Solve this type of problem 5. 12^3   Show Answer A: 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

Problem : 6 [ Algebraic Expression ]       Solve this type of problem 6. 34^2 - 32^2   Show Answer A: 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

Problem : 7 [ Algebraic Expression ]       Solve this type of problem 7. 9^3   Show Answer A: 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

Problem : 8 [ Algebraic Expression ]       Solve this type of problem 8. 10^3 - 7^3 - 3^3   Show Answer A: 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

Problem : 9 [ Algebraic Expression ]       Solve this type of problem 9. 4^3 + 3^3   Show Answer A: 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