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

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

Evaluate

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

Solution Steps

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

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

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

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

Multiply -1 and -1 to get 1.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

Apply the distributive property by multiplying each term of y\left(-y\right)+2y+y^{3}-2y^{2} by each term of 2+y.

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

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

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

Combine 2y^{3} and -2y^{3} to get 0.

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

Multiply 2 and -1 to get -2.

$$-2yy-yy^{2}+4y-2y^{2}+y^{4}$$

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

$$-2y^{2}-yy^{2}+4y-2y^{2}+y^{4}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

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

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

Expand

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

Solution Steps

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

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

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

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

Multiply -1 and -1 to get 1.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

Apply the distributive property by multiplying each term of y\left(-y\right)+2y+y^{3}-2y^{2} by each term of 2+y.

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

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

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

Combine 2y^{3} and -2y^{3} to get 0.

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

Multiply 2 and -1 to get -2.

$$-2yy-yy^{2}+4y-2y^{2}+y^{4}$$

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

$$-2y^{2}-yy^{2}+4y-2y^{2}+y^{4}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

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

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