Answer
$(a-8b)(a+4b)$
Work Step by Step
To factor a trinomial in the form $x^2+bx+c$, we must find two numbers whose product is $c$ and whose sum is $b$. We then insert these two numbers into the blanks of the factors $(x+\_)(x+\_)$. [In the case of this problem, the main variable is $a$, not $x$]
In the case of $a^2-4ab-32b^2$, we are looking for two numbers whose product is $-32b^2$ and whose sum is $-4b$. The numbers $-8b$ and $4b$ meet these criteria, because $$-8b\times4b=-32b^2\;\text{and}\;-8b+4b=-4b$$When we insert these numbers into the blanks, we arrive at the factors $(a-8b)(a+4b)$.
