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-r^{2}+5rs-s^{2}

$−r_{2}+5rs−s_{2}$

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-r^{2}+5rs-s^{2}

$−r_{2}+5rs−s_{2}$

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r^{2}+rs-2r^{2}+rs-s\left(s-3r\right)

Use the distributive property to multiply r by r+s.

-r^{2}+rs+rs-s\left(s-3r\right)

Combine r^{2} and -2r^{2} to get -r^{2}.

-r^{2}+2rs-s\left(s-3r\right)

Combine rs and rs to get 2rs.

-r^{2}+2rs-\left(s^{2}-3sr\right)

Use the distributive property to multiply s by s-3r.

-r^{2}+2rs-s^{2}+3sr

To find the opposite of s^{2}-3sr, find the opposite of each term.

-r^{2}+5rs-s^{2}

Combine 2rs and 3sr to get 5rs.

r^{2}+rs-2r^{2}+rs-s\left(s-3r\right)

Use the distributive property to multiply r by r+s.

-r^{2}+rs+rs-s\left(s-3r\right)

Combine r^{2} and -2r^{2} to get -r^{2}.

-r^{2}+2rs-s\left(s-3r\right)

Combine rs and rs to get 2rs.

-r^{2}+2rs-\left(s^{2}-3sr\right)

Use the distributive property to multiply s by s-3r.

-r^{2}+2rs-s^{2}+3sr

To find the opposite of s^{2}-3sr, find the opposite of each term.

-r^{2}+5rs-s^{2}

Combine 2rs and 3sr to get 5rs.