Question

Factor the difference of squares 9(x-3)^2 -49

Answer 1

`\textit{difference of squares} \\\\ (a-b)(a+b) = a^2-b^2 \\\\[-0.35em] ~\dotfill\\\\ 9(x-3)^2 - 49\implies 3^2(x-3)^2 - 49\implies 3^2(x-3)^2 -7^2 \\\\\\ ( ~~ 3(x-3) ~~ )^2-7^2\implies ( ~~ 3(x-3)-7 ~~ )( ~~ 3(x-3)+7 ~~ ) \\\\\\ (3x-9~~ - ~~7)(3x-9~~ + ~~7)\implies (3x-16)(3x-2)`