Solve 3r(r-2s)-s(2r-3s)-(3r^2-8rs)

$$3 r ( r - 2 s ) - s ( 2 r - 3 s ) - ( 3 r ^ { 2 } - 8 r s )$$

Evaluate

$$3s^{2}$$

Solution Steps

Use the distributive property to multiply 3r by r-2s.

$$3r^{2}-6rs-s\left(2r-3s\right)-\left(3r^{2}-8rs\right)$$

Use the distributive property to multiply s by 2r-3s.

$$3r^{2}-6rs-\left(2sr-3s^{2}\right)-\left(3r^{2}-8rs\right)$$

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

$$3r^{2}-6rs-2sr+3s^{2}-\left(3r^{2}-8rs\right)$$

Combine -6rs and -2sr to get -8rs.

$$3r^{2}-8rs+3s^{2}-\left(3r^{2}-8rs\right)$$

To find the opposite of 3r^{2}-8rs, find the opposite of each term.

$$3r^{2}-8rs+3s^{2}-3r^{2}+8rs$$

Combine 3r^{2} and -3r^{2} to get 0.

$$-8rs+3s^{2}+8rs$$

Combine -8rs and 8rs to get 0.

$$3s^{2}$$

Expand

$$3s^{2}$$

Solution Steps

Use the distributive property to multiply 3r by r-2s.

$$3r^{2}-6rs-s\left(2r-3s\right)-\left(3r^{2}-8rs\right)$$

Use the distributive property to multiply s by 2r-3s.

$$3r^{2}-6rs-\left(2sr-3s^{2}\right)-\left(3r^{2}-8rs\right)$$

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

$$3r^{2}-6rs-2sr+3s^{2}-\left(3r^{2}-8rs\right)$$

Combine -6rs and -2sr to get -8rs.

$$3r^{2}-8rs+3s^{2}-\left(3r^{2}-8rs\right)$$

To find the opposite of 3r^{2}-8rs, find the opposite of each term.

$$3r^{2}-8rs+3s^{2}-3r^{2}+8rs$$

Combine 3r^{2} and -3r^{2} to get 0.

$$-8rs+3s^{2}+8rs$$

Combine -8rs and 8rs to get 0.

$$3s^{2}$$