Question

($a^2$ + $b^2$) $\times$ (${-a}^2$ + $b^2$) =

• A. $-a^4+b^4$
• B. $a^2-b^2$
• C. $a^4-b^4$
• D. $b^4+a^4$

Answer 1

The correct option is A $-a^4+b^4$

- $a^2$ + $b^2$ = $b^2$ - $a^2$
$a^2$ + $b^2$ = $b^2$ + $a^2$ (commutative law)

So, ($a^2$ + $b^2$)(-$a^2$ + $b^2$)
= ($b^2$ + $a^2$)($b^2$ - $a^2$)

$(x+y)(x-y)$ = ($x^2$ - $y^2$) (Identity)

So, ($b^2$ + $a^2$)($b^2$ - $a^2$)
= $(b^2{)}^2-(a^2{)}^2$
= $b^4$ - $a^4$