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

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

Evaluate

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

Solution Steps

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

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

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

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

Combine rs and rs to get 2rs.

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

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

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

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

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

Combine 2rs and 3sr to get 5rs.

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

Expand

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

Solution Steps

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

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

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

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

Combine rs and rs to get 2rs.

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

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

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

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

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

Combine 2rs and 3sr to get 5rs.

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