The product in simplest form is (x - 4)
Solution:
Given expression is:
[tex]\frac{8}{2x+8} \times \frac{x^2-16}{4}[/tex]
We have to find the product in simplest form
In the given expression,
2x + 8 = 2(x+ 4)
We know that,
[tex]a^2-b^2=(a+b)(a-b)[/tex]
Therefore,
[tex]x^2-16 = x^2-4^2 =(x+4)(x-4)[/tex]
Substitute these in given expression
[tex]\frac{8}{2(x+4)} \times \frac{(x+4)(x-4)}{4}[/tex]
Cancel the common factors,
[tex]\frac{8}{2(x+4)} \times \frac{(x+4)(x-4)}{4} = x - 4[/tex]
Thus the product in simplest form is (x - 4)
