Solve (2-y)^2-y(y+5)

$$( 2 - y ) ^ { 2 } - y ( y + 5 )$$

Evaluate

$$4-9y$$

Solution Steps

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

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

Use the distributive property to multiply y by y+5.

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

To find the opposite of y^{2}+5y, find the opposite of each term.

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

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

$$4-4y-5y$$

Combine -4y and -5y to get -9y.

$$4-9y$$

Expand

$$4-9y$$

Solution Steps

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

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

Use the distributive property to multiply y by y+5.

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

To find the opposite of y^{2}+5y, find the opposite of each term.

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

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

$$4-4y-5y$$

Combine -4y and -5y to get -9y.

$$4-9y$$