Question

What is (1/2x-5)^2 simplified?

Answer 1

$\frac{x^2}{4}-\frac{10x}{2}+25$

Solution:

Given expression is $(\frac{1}{2}x-5)^2$.

Simplify the expression using algebraic formula $(a-b)^2=a^2-2ab+b^2$

$(\frac{1}{2}x-5)^2=(\frac{x}{2}-5)^2$

               $=(\frac{x}{2})^2-2(\frac{x}{2})5+5^2$

               $=\frac{x^2}{4}-10(\frac{x}{2})+25$

               $=\frac{x^2}{4}-\frac{10x}{2}+25$

$(\frac{1}{2}x-5)^2=\frac{x^2}{4}-\frac{10x}{2}+25$.

Hence, the simplified form of  $(\frac{1}{2}x-5)^2$ is $\frac{x^2}{4}-\frac{10x}{2}+25$.