Question

17. Simplify each of the following:
(i) (x + 3)^3 +
(x - 3)^3

​

Answer 1

$\sf{(x+3)^3+(x-3)^3}$

We know,

◘ $\sl{(a+b)^3=a^3+3a^2b+3ab^2+b^3}$

◘ $\sl{(a-b)^3=a^3-3a^2b+3ab^2-b^3}$

Putting the formulae in the given expression :-

$\sf{\hookrightarrow [x^3+3\times3x^2+3x(3)^2+3^3]+[x^3-3\times3x^2+3x(3)^2-(3)^2]}\\\\\sf{\hookrightarrow x^3+9x^2+27x+9+x^3-9x^2+27x-9}\\\\\sf{\hookrightarrow x^3+x^3+9x^2-9x^2+27x+27x+9-9}\\\\\sf{\hookrightarrow 2x^3+54x}\\\\\sf{\hookrightarrow 2x(x^2+27)}$