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

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

Evaluate

$$-2\left(y+1\right)\left(y+6\right)$$

Solution Steps

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

$$-3\left(4+4y+y^{2}\right)+y\left(y-2\right)$$

Use the distributive property to multiply -3 by 4+4y+y^{2}.

$$-12-12y-3y^{2}+y\left(y-2\right)$$

Use the distributive property to multiply y by y-2.

$$-12-12y-3y^{2}+y^{2}-2y$$

Combine -3y^{2} and y^{2} to get -2y^{2}.

$$-12-12y-2y^{2}-2y$$

Combine -12y and -2y to get -14y.

$$-12-14y-2y^{2}$$

Expand

$$-2y^{2}-14y-12$$

Solution Steps

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

$$-3\left(4+4y+y^{2}\right)+y\left(y-2\right)$$

Use the distributive property to multiply -3 by 4+4y+y^{2}.

$$-12-12y-3y^{2}+y\left(y-2\right)$$

Use the distributive property to multiply y by y-2.

$$-12-12y-3y^{2}+y^{2}-2y$$

Combine -3y^{2} and y^{2} to get -2y^{2}.

$$-12-12y-2y^{2}-2y$$

Combine -12y and -2y to get -14y.

$$-12-14y-2y^{2}$$