Question

Simplify the given algebraic expression:
$n^2(n-2)+2n^3(n+3)-6n(n-4)$

• A. $2n^4+7n^3-8n^2+24n$
• B. $n^4+5n^3-8n^2+24n$
• C. $2n^4+7n^3-4n^2+6n$
• D. $n^4+5n^3-4n^2+24n$

Answer 1

The correct option is A $2n^4+7n^3-8n^2+24n$

$n^2(n-2)+2n^3(n+3)-6n(n-4)$
(Using $a^m\times a^n=a^{(m+n)}$)
$=(n^{2+1}-2n^2)+(2n^{3+1}+6n^3)-(6n^{1+1}-24n)$
$=n^3-2n^2+2n^4+6n^3-6n^2+24n$
(Grouping the like terms)
$=2n^4+7n^3-8n^2+24n$