Question

Factorize $x^2-4x+4$.

Answer 1

Factorize${\mathit{x}}^{\mathbf{2}}\mathbf{-}\mathbf{4}\mathit{x}\mathbf{+}\mathbf{4}$.

We can write the given expression as

$x^2-4x+4=x^2-2x-2x+4$

$=x\left(x-2\right)-2\left(x-2\right)$ [ taking common terms out ]

$=\left(x-2\right)\left(x-2\right)$

$={\left(x-2\right)}^2$

Hence, the factored expression is${\left(x-2\right)}^{\mathbf{2}}$.