Question

How do you factorize $a^2-2ab+b^2$?

Answer 1

Factorize the given expression using the common factor method:

The given expression is $a^2-2ab+b^2$.

It can be factorized as follows,

$a^2-2ab+b^2=a^2-ab-ab+b^2$

$\Rightarrow a^2-2ab+b^2=\left(a^2-ab\right)-\left(ab-b^2\right)$

$\Rightarrow a^2-2ab+b^2=a\left(a-b\right)-b\left(a-b\right)$

$\Rightarrow a^2-2ab+b^2=\left(a-b\right)\left(a-b\right)$

Hence, the factors of $a^2-2ab+b^2$ obtained by using the common factor method is $\left(a-b\right)\left(a-b\right)$.