Question

factor the expression 64a^2-b^2

Answer 1

Its a difference of two squares, something you should recognize and always be looking for when factoring
(8a-b)(8a-b)
(8a-b)^2

Answer 2

\[
64a^2= 8^2a^2 = (8a)^2
\]So we have \[
(8a)^2-b^2
\]Difference of squares.

Answer 3

Difference of squares says: \[
\color{red}c^2-\color{blue}d^2 = (\color{red}c-\color{blue}d)(\color{red}c+\color{blue}d)
\]But in our case we have \(c=8a\) and \(d=b\).\[
(\color{red}{8a})^2-\color{blue}b^2 = (\color{red}{8a}-\color{blue}b)(\color{red}{8a}+\color{blue}b)
\]