Question

Express the product in simplest form.

Answer 1

The product in simplest form is (x - 4)

Solution:

Given expression is:

$\frac{8}{2x+8} \times \frac{x^2-16}{4}$

We have to find the product in simplest form

In the given expression,

2x + 8 = 2(x+ 4)

We know that,

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

Therefore,

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

Substitute these in given expression

$\frac{8}{2(x+4)} \times \frac{(x+4)(x-4)}{4}$

Cancel the common factors,

$\frac{8}{2(x+4)} \times \frac{(x+4)(x-4)}{4} = x - 4$

Thus the product in simplest form is (x - 4)