Solve (y-2)(y2+2y+4)-(y2+1)(y-1)

$$( y - 2 ) ( y 2 + 2 y + 4 ) - ( y 2 + 1 ) ( y - 1 )$$

Evaluate

$$2y^{2}-y-y_{2}-7$$

Solution Steps

Apply the distributive property by multiplying each term of y-2 by each term of y_{2}+2y+4.

$$yy_{2}+2y^{2}+4y-2y_{2}-4y-8-\left(y_{2}+1\right)\left(y-1\right)$$

Combine 4y and -4y to get 0.

$$yy_{2}+2y^{2}-2y_{2}-8-\left(y_{2}+1\right)\left(y-1\right)$$

Apply the distributive property by multiplying each term of y_{2}+1 by each term of y-1.

$$yy_{2}+2y^{2}-2y_{2}-8-\left(y_{2}y-y_{2}+y-1\right)$$

To find the opposite of y_{2}y-y_{2}+y-1, find the opposite of each term.

$$yy_{2}+2y^{2}-2y_{2}-8-y_{2}y-\left(-y_{2}\right)-y-\left(-1\right)$$

The opposite of -y_{2} is y_{2}.

$$yy_{2}+2y^{2}-2y_{2}-8-y_{2}y+y_{2}-y-\left(-1\right)$$

The opposite of -1 is 1.

$$yy_{2}+2y^{2}-2y_{2}-8-y_{2}y+y_{2}-y+1$$

Combine yy_{2} and -y_{2}y to get 0.

$$2y^{2}-2y_{2}-8+y_{2}-y+1$$

Combine -2y_{2} and y_{2} to get -y_{2}.

$$2y^{2}-y_{2}-8-y+1$$

Add -8 and 1 to get -7.

$$2y^{2}-y_{2}-7-y$$

Expand

$$2y^{2}-y-y_{2}-7$$

Solution Steps

Apply the distributive property by multiplying each term of y-2 by each term of y_{2}+2y+4.

$$yy_{2}+2y^{2}+4y-2y_{2}-4y-8-\left(y_{2}+1\right)\left(y-1\right)$$

Combine 4y and -4y to get 0.

$$yy_{2}+2y^{2}-2y_{2}-8-\left(y_{2}+1\right)\left(y-1\right)$$

Apply the distributive property by multiplying each term of y_{2}+1 by each term of y-1.

$$yy_{2}+2y^{2}-2y_{2}-8-\left(y_{2}y-y_{2}+y-1\right)$$

To find the opposite of y_{2}y-y_{2}+y-1, find the opposite of each term.

$$yy_{2}+2y^{2}-2y_{2}-8-y_{2}y-\left(-y_{2}\right)-y-\left(-1\right)$$

The opposite of -y_{2} is y_{2}.

$$yy_{2}+2y^{2}-2y_{2}-8-y_{2}y+y_{2}-y-\left(-1\right)$$

The opposite of -1 is 1.

$$yy_{2}+2y^{2}-2y_{2}-8-y_{2}y+y_{2}-y+1$$

Combine yy_{2} and -y_{2}y to get 0.

$$2y^{2}-2y_{2}-8+y_{2}-y+1$$

Combine -2y_{2} and y_{2} to get -y_{2}.

$$2y^{2}-y_{2}-8-y+1$$

Add -8 and 1 to get -7.

$$2y^{2}-y_{2}-7-y$$