Question

(a $-$ b)² + 8(a $-$ b) + 15

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}{\left(a-b\right)}^2+8\left(a-b\right)+15 \\ ={\left(a-b\right)}^2+5\left(a-b\right)+3\left(a-b\right)+15 \\ =\left(a-b\right)\left[\left(a-b\right)+5\right]+3\left[\left(a-b\right)+5\right] \\ =\left[\left(a-b\right)+5\right]\left[\left(a-b\right)+3\right] \\ =\left(a-b+5\right)\left(a-b+3\right) \end{gathered}$$