Question

Perform the multiplication
(a–5)^2(5+a)^2

Answer 1

`\bf \textit{difference of squares} \\\\ (a-b)(a+b) = a^2-b^2 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (a-5)^2(5+a)^2\implies (a-5)^2(a+5)^2\implies [(a-5)(a+5)]^2\implies \stackrel{\stackrel{\textit{difference}}{\textit{of squares}}}{[a^2-5^2]^2} \\[2em] [a^2-25]^2\implies (a^2-25)(a^2-25)\implies \stackrel{\mathbb{F~O~I~L}}{a^4-50a^2+25^2}\implies a^4-50a^2+625`