Question

How to factor z²-4z+4

Answer 1

$\implies {\blue {\boxed {\boxed {\purple {\sf { \: ({ \: z - 2 \: })^{2} \: }}}}}}$

$\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}$

${z}^{2} - 4z + 4$

$= {z}^{2} - 2z - 2z + 4$

Taking "$z$" as common from first two terms and "$2$" from last two terms, we have

$= z \: ( \: z - 2 \: ) - 2 \: ( \: z - 2 \: )$

Taking the factor $(z-2)$ as common,

$= ( \: z - 2 \: )( \: z - 2 \: )$

$= {( \: z - 2 \: )}^{1 + 1}$

$= ({ \: z - 2 \: })^{2}$

$\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35❦}}}}}$