Question

What is the factorised expression for $x^3-27$?

• A. $(x-3)(x^2+3x+9)$
• B. $(x+3)(x^2+3x+9)$
• C. $(x-3)(x^2-3x+9)$
• D. $(x-3)(x^2+3x-9)$

Answer 1

The correct option is A

$(x-3)(x^2+3x+9)$

$(x^3-27)$$=x^3-3^3$
$Weknowthat,a^3-b^3=(a-b)(a^2+ab+b^2)$
$\Rightarrow x^3-3^3=(x-3)(x^2+3x+3^2)$
$=(x-3)(x^2+3x+9)$