Question

Is the following expression true or false? Show your work.

[x^2 + 8x + 16] · [x^2 – 8x + 16] = (x^2 – 16)^2

Answer 1

The expression is true.

Step-by-step explanation:

`(x^2+8x+16)(x^2-8x+16)=(x+4)^2(x-4)^2=((x+4)(x-4))^2`

We know that (a +b)(a-b) = a²-b²

So we have ,

`((x+4)(x-4))^2=(x^2-4^2)^2=(x^2-16)^2`

Which is Right Hand Side given.

So, the expression is true.