Question

Factorize: $x^3-(x-z{)}^3$

• A. $z(3x^2-3xz+z^2)$
• B. $y(3x^2-3xz+z^2)$
• C. $x(3x^2-3xz+z^2)$
• D. $z(3x^3-3xz+z^2)$

Answer 1

The correct option is A

$z(3x^2-3xz+z^2)$

We know that

$a^3-b^3=(a-b)(a^2+ab+b^2)so,x^3-(x-z{)}^3=[x-(x-z\left)\right][x^2+x(x-z)+(x-z^2\left)\right]=(x-x+z\left)\right(x^2+x^2-xz+x^2+z^2-2xz)=z(3x^2-3xz+z^2)$