Solve y(1y^{2}+5y-7)+2(y^3-4y^2+0)+3(6y-5y^2-3y^3)

$$y ( 1 y ^ { 2 } + 5 y - 7 ) + 2 ( y ^ { 3 } - 4 y ^ { 2 } + 0 ) + 3 ( 6 y - 5 y ^ { 2 } - 3 y ^ { 3 } )$$

Evaluate

$$y\left(11-18y-6y^{2}\right)$$

Solution Steps

Use the distributive property to multiply y by 1y^{2}+5y-7.

$$y^{3}+5y^{2}-7y+2\left(y^{3}-4y^{2}+0\right)+3\left(6y-5y^{2}-3y^{3}\right)$$

Anything plus zero gives itself.

$$y^{3}+5y^{2}-7y+2\left(y^{3}-4y^{2}\right)+3\left(6y-5y^{2}-3y^{3}\right)$$

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

$$y^{3}+5y^{2}-7y+2y^{3}-8y^{2}+3\left(6y-5y^{2}-3y^{3}\right)$$

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

$$3y^{3}+5y^{2}-7y-8y^{2}+3\left(6y-5y^{2}-3y^{3}\right)$$

Combine 5y^{2} and -8y^{2} to get -3y^{2}.

$$3y^{3}-3y^{2}-7y+3\left(6y-5y^{2}-3y^{3}\right)$$

Use the distributive property to multiply 3 by 6y-5y^{2}-3y^{3}.

$$3y^{3}-3y^{2}-7y+18y-15y^{2}-9y^{3}$$

Combine -7y and 18y to get 11y.

$$3y^{3}-3y^{2}+11y-15y^{2}-9y^{3}$$

Combine -3y^{2} and -15y^{2} to get -18y^{2}.

$$3y^{3}-18y^{2}+11y-9y^{3}$$

Combine 3y^{3} and -9y^{3} to get -6y^{3}.

$$-6y^{3}-18y^{2}+11y$$

Expand

$$11y-18y^{2}-6y^{3}$$

Solution Steps

Use the distributive property to multiply y by 1y^{2}+5y-7.

$$y^{3}+5y^{2}-7y+2\left(y^{3}-4y^{2}+0\right)+3\left(6y-5y^{2}-3y^{3}\right)$$

Anything plus zero gives itself.

$$y^{3}+5y^{2}-7y+2\left(y^{3}-4y^{2}\right)+3\left(6y-5y^{2}-3y^{3}\right)$$

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

$$y^{3}+5y^{2}-7y+2y^{3}-8y^{2}+3\left(6y-5y^{2}-3y^{3}\right)$$

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

$$3y^{3}+5y^{2}-7y-8y^{2}+3\left(6y-5y^{2}-3y^{3}\right)$$

Combine 5y^{2} and -8y^{2} to get -3y^{2}.

$$3y^{3}-3y^{2}-7y+3\left(6y-5y^{2}-3y^{3}\right)$$

Use the distributive property to multiply 3 by 6y-5y^{2}-3y^{3}.

$$3y^{3}-3y^{2}-7y+18y-15y^{2}-9y^{3}$$

Combine -7y and 18y to get 11y.

$$3y^{3}-3y^{2}+11y-15y^{2}-9y^{3}$$

Combine -3y^{2} and -15y^{2} to get -18y^{2}.

$$3y^{3}-18y^{2}+11y-9y^{3}$$

Combine 3y^{3} and -9y^{3} to get -6y^{3}.

$$-6y^{3}-18y^{2}+11y$$