Solve 7(r-s)^2+4(2r-2s)

$$7 ( r - s ) ^ { 2 } + 4 ( 2 r - 2 s )$$

Evaluate

$$\left(r-s\right)\left(7r-7s+8\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(r-s\right)^{2}.

$$7\left(r^{2}-2rs+s^{2}\right)+4\left(2r-2s\right)$$

Use the distributive property to multiply 7 by r^{2}-2rs+s^{2}.

$$7r^{2}-14rs+7s^{2}+4\left(2r-2s\right)$$

Use the distributive property to multiply 4 by 2r-2s.

$$7r^{2}-14rs+7s^{2}+8r-8s$$

Expand

$$7r^{2}-14rs+8r+7s^{2}-8s$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(r-s\right)^{2}.

$$7\left(r^{2}-2rs+s^{2}\right)+4\left(2r-2s\right)$$

Use the distributive property to multiply 7 by r^{2}-2rs+s^{2}.

$$7r^{2}-14rs+7s^{2}+4\left(2r-2s\right)$$

Use the distributive property to multiply 4 by 2r-2s.

$$7r^{2}-14rs+7s^{2}+8r-8s$$