Solve r^2-(r-6)^2+3(r+5)=

$$r ^ { 2 } - ( r - 6 ) ^ { 2 } + 3 ( r + 5 ) =$$

Evaluate

$$15r-21$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(r-6\right)^{2}.

$$r^{2}-\left(r^{2}-12r+36\right)+3\left(r+5\right)$$

To find the opposite of r^{2}-12r+36, find the opposite of each term.

$$r^{2}-r^{2}+12r-36+3\left(r+5\right)$$

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

$$12r-36+3\left(r+5\right)$$

Use the distributive property to multiply 3 by r+5.

$$12r-36+3r+15$$

Combine 12r and 3r to get 15r.

$$15r-36+15$$

Add -36 and 15 to get -21.

$$15r-21$$

Expand

$$15r-21$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(r-6\right)^{2}.

$$r^{2}-\left(r^{2}-12r+36\right)+3\left(r+5\right)$$

To find the opposite of r^{2}-12r+36, find the opposite of each term.

$$r^{2}-r^{2}+12r-36+3\left(r+5\right)$$

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

$$12r-36+3\left(r+5\right)$$

Use the distributive property to multiply 3 by r+5.

$$12r-36+3r+15$$

Combine 12r and 3r to get 15r.

$$15r-36+15$$

Add -36 and 15 to get -21.

$$15r-21$$