Question

$16x^5-144x^3$ =

• A. $16x^3(x-3)(x-3)$
• B. $16x^5(1-9x^2)$
• C. $16x^3(3+x)(3-x)$
• D. $16x^3(x+3)(x-3)$

Answer 1

The correct option is D $16x^3(x+3)(x-3)$

The given expression $16x^5-144x^3$ can be written as,
$16x^3\times x^2-16\times 9\times x^3$
= $16x^3\times x^2-16x^3\times 9$
= $16x^3(x^2-9)$
= $16x^3(x^2-3^2)$
Using the identity : $a^2-b^2=(a+b)(a-b),$ we get,
$16x^3(x+3)(x-3)$