Question

Express the product in simplest form.

8/2x+8*x^2-16/4

A. (x + 4)
B. 2(x − 4)
C. (x − 4)
D. (x + 4)(x − 4)

Answer 1

The product in simplest form is (x - 4)

Solution:

Given expression is:

`(8)/(2x+8) * (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

`(8)/(2(x+4)) * ((x+4)(x-4))/(4)`

Cancel the common factors,

`(8)/(2(x+4)) * ((x+4)(x-4))/(4) = x - 4`

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