Solve 9y^2-(1+2y)^2=

$$9 y ^ { 2 } - ( 1 + 2 y ) ^ { 2 } =$$

Evaluate

$$\left(y-1\right)\left(5y+1\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(1+2y\right)^{2}.

$$9y^{2}-\left(1+4y+4y^{2}\right)$$

To find the opposite of 1+4y+4y^{2}, find the opposite of each term.

$$9y^{2}-1-4y-4y^{2}$$

Combine 9y^{2} and -4y^{2} to get 5y^{2}.

$$5y^{2}-1-4y$$

Expand

$$5y^{2}-4y-1$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(1+2y\right)^{2}.

$$9y^{2}-\left(1+4y+4y^{2}\right)$$

To find the opposite of 1+4y+4y^{2}, find the opposite of each term.

$$9y^{2}-1-4y-4y^{2}$$

Combine 9y^{2} and -4y^{2} to get 5y^{2}.

$$5y^{2}-1-4y$$