Question

Simplify the following rational expression and express in expanded form.

Answer 1

The solution for given expression is $\frac{(z + 2y)}{4}$

Solution:

Given that rational expression is:

$\frac{z^{2}+4 z y+4 y^{2}}{4 z+8 y}$

Taking "4" as common term from denominator,

$\frac{z^{2}+4 z y+4 y^{2}}{4(z + 2y)}$  ------- eqn 1

Let us use a algebraic identity which is as follows:

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

So, $z^{2}+4 z y+4 y^{2}$ can be expressed as:

$z^{2}+4 z y+4 y^{2} = (z + 2y)^2$

Substitute the above equation in eqn 1,

$\frac{(z + 2y)^2}{4(z + 2y)}$

Cancelling (z + 2y) in numerator and denominator

$\rightarrow \frac{(z + 2y)}{4}$

Thus the solution for given expression is $\frac{(z + 2y)}{4}$