Solve (y-3)(y-1)(y+1)(y+3)

$$(y-3)(y-1)(y+1)(y+3)$$

Evaluate

$$y^{4}-10y^{2}+9$$

Solution Steps

Apply the distributive property by multiplying each term of y-3 by each term of y-1.

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

Combine -y and -3y to get -4y.

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

Apply the distributive property by multiplying each term of y^{2}-4y+3 by each term of y+1.

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

Combine y^{2} and -4y^{2} to get -3y^{2}.

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

Combine -4y and 3y to get -y.

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

Apply the distributive property by multiplying each term of y^{3}-3y^{2}-y+3 by each term of y+3.

$$y^{4}+3y^{3}-3y^{3}-9y^{2}-y^{2}-3y+3y+9$$

Combine 3y^{3} and -3y^{3} to get 0.

$$y^{4}-9y^{2}-y^{2}-3y+3y+9$$

Combine -9y^{2} and -y^{2} to get -10y^{2}.

$$y^{4}-10y^{2}-3y+3y+9$$

Combine -3y and 3y to get 0.

$$y^{4}-10y^{2}+9$$

Expand

$$y^{4}-10y^{2}+9$$

Solution Steps

Apply the distributive property by multiplying each term of y-3 by each term of y-1.

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

Combine -y and -3y to get -4y.

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

Apply the distributive property by multiplying each term of y^{2}-4y+3 by each term of y+1.

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

Combine y^{2} and -4y^{2} to get -3y^{2}.

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

Combine -4y and 3y to get -y.

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

Apply the distributive property by multiplying each term of y^{3}-3y^{2}-y+3 by each term of y+3.

$$y^{4}+3y^{3}-3y^{3}-9y^{2}-y^{2}-3y+3y+9$$

Combine 3y^{3} and -3y^{3} to get 0.

$$y^{4}-9y^{2}-y^{2}-3y+3y+9$$

Combine -9y^{2} and -y^{2} to get -10y^{2}.

$$y^{4}-10y^{2}-3y+3y+9$$

Combine -3y and 3y to get 0.

$$y^{4}-10y^{2}+9$$