Solve y^2left(y-1right)^2+7y(-y+1)

$${ y }^{ 2 } { \left(y-1 \right) }^{ 2 } +7y(-y+1)$$

Evaluate

$$y\left(y-1\right)\left(y^{2}-y-7\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-1\right)^{2}.

$$y^{2}\left(y^{2}-2y+1\right)+7y\left(-y+1\right)$$

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

$$y^{4}-2y^{3}+y^{2}+7y\left(-y+1\right)$$

Use the distributive property to multiply 7y by -y+1.

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

Multiply y and y to get y^{2}.

$$y^{4}-2y^{3}+y^{2}+7y^{2}\left(-1\right)+7y$$

Multiply 7 and -1 to get -7.

$$y^{4}-2y^{3}+y^{2}-7y^{2}+7y$$

Combine y^{2} and -7y^{2} to get -6y^{2}.

$$y^{4}-2y^{3}-6y^{2}+7y$$

Expand

$$y^{4}-2y^{3}-6y^{2}+7y$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-1\right)^{2}.

$$y^{2}\left(y^{2}-2y+1\right)+7y\left(-y+1\right)$$

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

$$y^{4}-2y^{3}+y^{2}+7y\left(-y+1\right)$$

Use the distributive property to multiply 7y by -y+1.

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

Multiply y and y to get y^{2}.

$$y^{4}-2y^{3}+y^{2}+7y^{2}\left(-1\right)+7y$$

Multiply 7 and -1 to get -7.

$$y^{4}-2y^{3}+y^{2}-7y^{2}+7y$$

Combine y^{2} and -7y^{2} to get -6y^{2}.

$$y^{4}-2y^{3}-6y^{2}+7y$$