Question

Factorize each of the following algebraic expression:
x² + 9y² − 6xy − 25a²

Answer 1

$$\begin{gathered} {\mathrm{x}}^2+9{\mathrm{y}}^2-6\mathrm{xy}-25{\mathrm{a}}^2 \\ =({\mathrm{x}}^2-6\mathrm{xy}+9{\mathrm{y}}^2)-25{\mathrm{a}}^2 \\ =[{\mathrm{x}}^2-2\times \mathrm{x}\times 3\mathrm{y}+(3\mathrm{y}{)}^2]-25{\mathrm{a}}^2 \\ =(\mathrm{x}-3\mathrm{y}{)}^2-(5\mathrm{a}{)}^2 \\ =[(\mathrm{x}-3\mathrm{y})-5\mathrm{a}\left]\right[(\mathrm{x}-3\mathrm{y})+5\mathrm{a}] \\ =(\mathrm{x}-3\mathrm{y}-5\mathrm{a}\left)\right(\mathrm{x}-3\mathrm{y}+5\mathrm{a}) \end{gathered}$$