Solve 181r^2-(9r+2y)^2=

$$181 r ^ { 2 } - ( 9 r + 2 y ) ^ { 2 } =$$

Evaluate

$$-\left(2y+9r\right)^{2}+181r^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(9r+2y\right)^{2}.

$$181r^{2}-\left(81r^{2}+36ry+4y^{2}\right)$$

To find the opposite of 81r^{2}+36ry+4y^{2}, find the opposite of each term.

$$181r^{2}-81r^{2}-36ry-4y^{2}$$

Combine 181r^{2} and -81r^{2} to get 100r^{2}.

$$100r^{2}-36ry-4y^{2}$$

Expand

$$100r^{2}-36ry-4y^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(9r+2y\right)^{2}.

$$181r^{2}-\left(81r^{2}+36ry+4y^{2}\right)$$

To find the opposite of 81r^{2}+36ry+4y^{2}, find the opposite of each term.

$$181r^{2}-81r^{2}-36ry-4y^{2}$$

Combine 181r^{2} and -81r^{2} to get 100r^{2}.

$$100r^{2}-36ry-4y^{2}$$