Solve (5+2y)(y-3)-(5-2y)^2

$$( 5 + 2 y ) ( y - 3 ) - ( 5 - 2 y ) ^ { 2 }$$

Evaluate

$$-2y^{2}+19y-40$$

Solution Steps

Use the distributive property to multiply 5+2y by y-3 and combine like terms.

$$-y-15+2y^{2}-\left(5-2y\right)^{2}$$

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

$$-y-15+2y^{2}-\left(25-20y+4y^{2}\right)$$

To find the opposite of 25-20y+4y^{2}, find the opposite of each term.

$$-y-15+2y^{2}-25+20y-4y^{2}$$

Subtract 25 from -15 to get -40.

$$-y-40+2y^{2}+20y-4y^{2}$$

Combine -y and 20y to get 19y.

$$19y-40+2y^{2}-4y^{2}$$

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

$$19y-40-2y^{2}$$

Expand

$$-2y^{2}+19y-40$$

Solution Steps

Use the distributive property to multiply 5+2y by y-3 and combine like terms.

$$-y-15+2y^{2}-\left(5-2y\right)^{2}$$

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

$$-y-15+2y^{2}-\left(25-20y+4y^{2}\right)$$

To find the opposite of 25-20y+4y^{2}, find the opposite of each term.

$$-y-15+2y^{2}-25+20y-4y^{2}$$

Subtract 25 from -15 to get -40.

$$-y-40+2y^{2}+20y-4y^{2}$$

Combine -y and 20y to get 19y.

$$19y-40+2y^{2}-4y^{2}$$

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

$$19y-40-2y^{2}$$