Solve left(4-yright)^2-y(y+1)

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

Evaluate

$$16-9y$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4-y\right)^{2}.

$$16-8y+y^{2}-y\left(y+1\right)$$

Use the distributive property to multiply y by y+1.

$$16-8y+y^{2}-\left(y^{2}+y\right)$$

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

$$16-8y+y^{2}-y^{2}-y$$

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

$$16-8y-y$$

Combine -8y and -y to get -9y.

$$16-9y$$

Expand

$$16-9y$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4-y\right)^{2}.

$$16-8y+y^{2}-y\left(y+1\right)$$

Use the distributive property to multiply y by y+1.

$$16-8y+y^{2}-\left(y^{2}+y\right)$$

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

$$16-8y+y^{2}-y^{2}-y$$

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

$$16-8y-y$$

Combine -8y and -y to get -9y.

$$16-9y$$