Question

Factorize each of the following algebraic expression:
25 − p² − q² − 2pq

Answer 1

$$\begin{gathered} 25-{\mathrm{p}}^2-{\mathrm{q}}^2-2\mathrm{pq} \\ =25-({\mathrm{p}}^2+2\mathrm{pq}+{\mathrm{q}}^2) \\ =5^2-({\mathrm{p}}^2+2\times \mathrm{p}\times \mathrm{q}+{\mathrm{q}}^2) \\ =5^2-(\mathrm{p}+\mathrm{q}{)}^2 \\ =[5-(\mathrm{p}+\mathrm{q})\left]\right[5+(\mathrm{p}+\mathrm{q})] \\ =(5-\mathrm{p}-\mathrm{q}\left)\right(5+\mathrm{p}+\mathrm{q}) \\ =-(\mathrm{p}+\mathrm{q}-5\left)\right(\mathrm{p}+\mathrm{q}+5) \end{gathered}$$