Question

Which expression is equivalent to 7a4 - 28?

A) -7(a2 + 2)(a2 + 2)



B) 7(a2 + 2)(a2 - 2)

Eliminate


C) 7(a2 + 2)(a2 + 2)



D) 7(a2 - 2)(a2 - 2)

Answer 1

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)`