Question

Factorize each of the following algebraic expression:
(x + 2)² − 6(x + 2) + 9

Answer 1

$$\begin{gathered} (\mathrm{x}+2{)}^2-6(\mathrm{x}+2)+9 \\ =(\mathrm{x}+2{)}^2-2\times (\mathrm{x}+2)\times 3+3^2 \\ =\left[\right(\mathrm{x}+2)-3{]}^2 \\ =(\mathrm{x}+2-3{)}^2 \\ =(\mathrm{x}-1{)}^2 \\ =(\mathrm{x}-1\left)\right(\mathrm{x}-1) \end{gathered}$$