Question

Factorize each of the following algebraic expression:
49 − a² + 8ab − 16b²

Answer 1

$$\begin{gathered} 49-{\mathrm{a}}^2+8\mathrm{ab}-16{\mathrm{b}}^2 \\ =49-({\mathrm{a}}^2-8\mathrm{ab}+16{\mathrm{b}}^2) \\ =49-[{\mathrm{a}}^2-2\times \mathrm{a}\times 4\mathrm{b}+(4\mathrm{b}{)}^2] \\ =7^2-(\mathrm{a}-4\mathrm{b}{)}^2 \\ =[7-(\mathrm{a}-4\mathrm{b}\left)\right][7+(\mathrm{a}-4\mathrm{b}\left)\right] \\ =(7-\mathrm{a}+4\mathrm{b})(7+\mathrm{a}-4\mathrm{b}) \\ =-(\mathrm{a}-4\mathrm{b}-7)(\mathrm{a}-4\mathrm{b}+7) \\ =-(\mathrm{a}-4\mathrm{b}+7)(\mathrm{a}-4\mathrm{b}-7) \end{gathered}$$