Question

Which expression is equivalent to 7a4 - 28?

Answer 1

ANSWER

B.

$7( {a}^{2} + 2)( {a}^{2} - 2)$

EXPLANATION

The given expression is

$7 {a}^{4} - 28$

First factor 7 to get,

$7 ({a}^{4} - 4)$

Write the expression in the parenthesis as difference of two squares:

$7 (({ {a}^{2} )}^{2} - 4)$

Recall that:

${x}^{2} - {y}^{2} = (x + y)(x - y)$

We apply this to our expression to get:

$7 (({ {a}^{2} )}^{2} - {2}^{2} ) = 7( {a}^{2} + 2)( {a}^{2} - 2)$