Solve left(y+2right)^2-9left(5-2yright)^2

$${ \left(y+2 \right) }^{ 2 } -9 { \left(5-2y \right) }^{ 2 }$$

Evaluate

$$\left(17-5y\right)\left(7y-13\right)$$

Solution Steps

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

$$y^{2}+4y+4-9\left(5-2y\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(5-2y\right)^{2}.

$$y^{2}+4y+4-9\left(25-20y+4y^{2}\right)$$

Use the distributive property to multiply -9 by 25-20y+4y^{2}.

$$y^{2}+4y+4-225+180y-36y^{2}$$

Subtract 225 from 4 to get -221.

$$y^{2}+4y-221+180y-36y^{2}$$

Combine 4y and 180y to get 184y.

$$y^{2}+184y-221-36y^{2}$$

Combine y^{2} and -36y^{2} to get -35y^{2}.

$$-35y^{2}+184y-221$$

Expand

$$-35y^{2}+184y-221$$

Solution Steps

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

$$y^{2}+4y+4-9\left(5-2y\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(5-2y\right)^{2}.

$$y^{2}+4y+4-9\left(25-20y+4y^{2}\right)$$

Use the distributive property to multiply -9 by 25-20y+4y^{2}.

$$y^{2}+4y+4-225+180y-36y^{2}$$

Subtract 225 from 4 to get -221.

$$y^{2}+4y-221+180y-36y^{2}$$

Combine 4y and 180y to get 184y.

$$y^{2}+184y-221-36y^{2}$$

Combine y^{2} and -36y^{2} to get -35y^{2}.

$$-35y^{2}+184y-221$$