Answer
$3a^2-8ab-15b^2$
Work Step by Step
The given expression, $
(5a^2-3ab-7b^2)-(2a^2+5ab+8b^2)
,$ simplifies to
\begin{align*}\require{cancel}
&
(5a^2-3ab-7b^2)-1(2a^2)-1(5ab)-1(8b^2)
&(\text{Use Distributive Property})
\\&=
5a^2-3ab-7b^2-2a^2-5ab-8b^2
\\&=
(5a^2-2a^2)+(-3ab-5ab)+(-7b^2-8b^2)
&(\text{combine like terms})
\\&=
3a^2-8ab-15b^2
.\end{align*}
Hence, the expression $(5a^2-3ab-7b^2)-(2a^2+5ab+8b^2)$ simplifies to $3a^2-8ab-15b^2$.
