Question

Simplify:
1.(a+b)^3-(a-b)^3
2.(a+2)^3-6a(a+2)

Answer 1

Answer:

8a3

Step by Step explanation

Given : (a+b)^3 + (a-b)^3 + 6a(a^2- b^2)(a+b)3+(a−b)3+6a(a2−b2)

To Find : Simplify

Solution :

(a+b)^3 + (a-b)^3 + 6a(a^2- b^2)(a+b)3+(a−b)3+6a(a2−b2)

Identity : (a+b)^3=a^3+b^3+3a^2 b+3ab^2(a+b)3=a3+b3+3a2b+3ab2

Identity : (a-b)^3=a^3-b^3-3a^2 b+3ab^2(a−b)3=a3−b3−3a2b+3ab2

a^3+b^3+3a^2 b+3ab^2+a^3-b^3-3a^2 b+3ab^2+ 6a^3- 6ab^2a3+b3+3a2b+3ab2+a3−b3−3a2b+3ab2+6a3−6ab2

8a^38a3

Hence (a+b)^3 + (a-b)^3 + 6a(a^2- b^2)(a+b)3+(a−b)3+6a(a2−b2) = 8a^38a3