Type a math problem

This site uses cookies for analytics, personalized content and ads. By continuing to browse this site, you agree to this use. Learn more

Type a math problem

Evaluate

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

$−r_{2}+5rs−s_{2}$

Solution Steps

r(r+s)-2r^2+rs-s(s-3r)

$r(r+s)−2r_{2}+rs−s(s−3r)$

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

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

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

$r_{2}+rs−2r_{2}+rs−s(s−3r)$

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

Combine $r_{2}$ and $−2r_{2}$ to get $−r_{2}$.

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

$−r_{2}+rs+rs−s(s−3r)$

Combine rs and rs to get 2rs.

Combine $rs$ and $rs$ to get $2rs$.

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

$−r_{2}+2rs−s(s−3r)$

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

Use the distributive property to multiply $s$ by $s−3r$.

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

$−r_{2}+2rs−(s_{2}−3sr)$

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

To find the opposite of $s_{2}−3sr$, find the opposite of each term.

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

$−r_{2}+2rs−s_{2}+3sr$

Combine 2rs and 3sr to get 5rs.

Combine $2rs$ and $3sr$ to get $5rs$.

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

$−r_{2}+5rs−s_{2}$

Expand

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

$−r_{2}+5rs−s_{2}$

Solution Steps

r(r+s)-2r^2+rs-s(s-3r)

$r(r+s)−2r_{2}+rs−s(s−3r)$

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

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

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

$r_{2}+rs−2r_{2}+rs−s(s−3r)$

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

Combine $r_{2}$ and $−2r_{2}$ to get $−r_{2}$.

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

$−r_{2}+rs+rs−s(s−3r)$

Combine rs and rs to get 2rs.

Combine $rs$ and $rs$ to get $2rs$.

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

$−r_{2}+2rs−s(s−3r)$

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

Use the distributive property to multiply $s$ by $s−3r$.

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

$−r_{2}+2rs−(s_{2}−3sr)$

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

To find the opposite of $s_{2}−3sr$, find the opposite of each term.

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

$−r_{2}+2rs−s_{2}+3sr$

Combine 2rs and 3sr to get 5rs.

Combine $2rs$ and $3sr$ to get $5rs$.

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

$−r_{2}+5rs−s_{2}$

Share

Copy

Copied to clipboard

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.

Back to top