Question

Which will result in a difference of squares?

(–7x + 4)(–7x + 4)
(–7x + 4)(4 – 7x)
(–7x + 4)(–7x – 4)
(–7x + 4)(7x – 4)

Answer 1

The third one (-7x+4)(-7x-4)

Answer 2

Expanding the given expressions using Foil:

1)(–7x + 4)(–7x + 4) =
`7x^(2)-28x-28x+16=49x^(2)-56x+16`

2) (–7x + 4)(4 – 7x)=
`-28x+49x^(2)+16-28x=49x^(2)-56x+16.`

3)(–7x + 4)(–7x – 4)=
`49x^(2)+28x-28x-16`=
`49x^(2)-16.`

4)(–7x + 4)(7x – 4)=
`49x^(2)+28x+28x-16=49x^(2)+56x-16.`

The third option that is (–7x + 4)(–7x – 4) is difference of two squares.