Solve -y(2y+9)(10-11y)

$$-y(2y+9)(10-11y)$$

Evaluate

$$-y\left(10-11y\right)\left(2y+9\right)$$

Solution Steps

Use the distributive property to multiply -y by 2y+9.

$$\left(2\left(-y\right)y+9\left(-y\right)\right)\left(10-11y\right)$$

Apply the distributive property by multiplying each term of 2\left(-y\right)y+9\left(-y\right) by each term of 10-11y.

$$20\left(-y\right)y-22\left(-y\right)y^{2}+90\left(-y\right)-99\left(-y\right)y$$

Multiply -22 and -1 to get 22.

$$20\left(-y\right)y+22yy^{2}+90\left(-y\right)-99\left(-y\right)y$$

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

$$20\left(-y\right)y+22y^{3}+90\left(-y\right)-99\left(-y\right)y$$

Multiply -99 and -1 to get 99.

$$20\left(-y\right)y+22y^{3}+90\left(-y\right)+99yy$$

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

$$20\left(-y\right)y+22y^{3}+90\left(-y\right)+99y^{2}$$

Multiply 20 and -1 to get -20.

$$-20yy+22y^{3}+90\left(-1\right)y+99y^{2}$$

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

$$-20y^{2}+22y^{3}+90\left(-1\right)y+99y^{2}$$

Multiply 90 and -1 to get -90.

$$-20y^{2}+22y^{3}-90y+99y^{2}$$

Combine -20y^{2} and 99y^{2} to get 79y^{2}.

$$79y^{2}+22y^{3}-90y$$

Expand

$$22y^{3}+79y^{2}-90y$$

Solution Steps

Use the distributive property to multiply -y by 2y+9.

$$\left(2\left(-y\right)y+9\left(-y\right)\right)\left(10-11y\right)$$

Apply the distributive property by multiplying each term of 2\left(-y\right)y+9\left(-y\right) by each term of 10-11y.

$$20\left(-y\right)y-22\left(-y\right)y^{2}+90\left(-y\right)-99\left(-y\right)y$$

Multiply -22 and -1 to get 22.

$$20\left(-y\right)y+22yy^{2}+90\left(-y\right)-99\left(-y\right)y$$

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

$$20\left(-y\right)y+22y^{3}+90\left(-y\right)-99\left(-y\right)y$$

Multiply -99 and -1 to get 99.

$$20\left(-y\right)y+22y^{3}+90\left(-y\right)+99yy$$

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

$$20\left(-y\right)y+22y^{3}+90\left(-y\right)+99y^{2}$$

Multiply 20 and -1 to get -20.

$$-20yy+22y^{3}+90\left(-1\right)y+99y^{2}$$

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

$$-20y^{2}+22y^{3}+90\left(-1\right)y+99y^{2}$$

Multiply 90 and -1 to get -90.

$$-20y^{2}+22y^{3}-90y+99y^{2}$$

Combine -20y^{2} and 99y^{2} to get 79y^{2}.

$$79y^{2}+22y^{3}-90y$$