Question

Factorize the following using appropriate identities: $4y^2-4y+1$.

Answer 1

Factorize the given polynomial

$4y^2-4y+1={\left(2y\right)}^2-2\times 2y\times 1+\left(1^2\right)$

Use the identity ${\mathbf{(}\mathbf{a}\mathbf{-}\mathbf{b}\mathbf{)}}^{\mathbf{2}}\mathbf{=}{\mathit{a}}^{\mathbf{2}}\mathbf{+}{\mathit{b}}^{\mathbf{2}}\mathbf{-}\mathbf{2}\mathit{a}\mathit{b}$

$4y^2-4y+1={(2y-1)}^2$

Hence, the factors of the polynomial $4y^2-4y+1$ are $2y-1$ and$2y-1$.