Solve 2(y-3)^2-6y(y-3)

$$2 ( y - 3 ) ^ { 2 } - 6 y ( y - 3 )$$

Evaluate

$$-2\left(y-3\right)\left(2y+3\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-3\right)^{2}.

$$2\left(y^{2}-6y+9\right)-6y\left(y-3\right)$$

Use the distributive property to multiply 2 by y^{2}-6y+9.

$$2y^{2}-12y+18-6y\left(y-3\right)$$

Use the distributive property to multiply -6y by y-3.

$$2y^{2}-12y+18-6y^{2}+18y$$

Combine 2y^{2} and -6y^{2} to get -4y^{2}.

$$-4y^{2}-12y+18+18y$$

Combine -12y and 18y to get 6y.

$$-4y^{2}+6y+18$$

Expand

$$18+6y-4y^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-3\right)^{2}.

$$2\left(y^{2}-6y+9\right)-6y\left(y-3\right)$$

Use the distributive property to multiply 2 by y^{2}-6y+9.

$$2y^{2}-12y+18-6y\left(y-3\right)$$

Use the distributive property to multiply -6y by y-3.

$$2y^{2}-12y+18-6y^{2}+18y$$

Combine 2y^{2} and -6y^{2} to get -4y^{2}.

$$-4y^{2}-12y+18+18y$$

Combine -12y and 18y to get 6y.

$$-4y^{2}+6y+18$$