Solve (3y-5)(y+4)-(y-3)(y-5)

$$( 3 y - 5 ) ( y + 4 ) - ( y - 3 ) ( y - 5 )$$

Evaluate

$$2y^{2}+15y-35$$

Solution Steps

Apply the distributive property by multiplying each term of 3y-5 by each term of y+4.

$$3y^{2}+12y-5y-20-\left(y-3\right)\left(y-5\right)$$

Combine 12y and -5y to get 7y.

$$3y^{2}+7y-20-\left(y-3\right)\left(y-5\right)$$

Apply the distributive property by multiplying each term of y-3 by each term of y-5.

$$3y^{2}+7y-20-\left(y^{2}-5y-3y+15\right)$$

Combine -5y and -3y to get -8y.

$$3y^{2}+7y-20-\left(y^{2}-8y+15\right)$$

To find the opposite of y^{2}-8y+15, find the opposite of each term.

$$3y^{2}+7y-20-y^{2}-\left(-8y\right)-15$$

The opposite of -8y is 8y.

$$3y^{2}+7y-20-y^{2}+8y-15$$

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

$$2y^{2}+7y-20+8y-15$$

Combine 7y and 8y to get 15y.

$$2y^{2}+15y-20-15$$

Subtract 15 from -20 to get -35.

$$2y^{2}+15y-35$$

Expand

$$2y^{2}+15y-35$$

Solution Steps

Apply the distributive property by multiplying each term of 3y-5 by each term of y+4.

$$3y^{2}+12y-5y-20-\left(y-3\right)\left(y-5\right)$$

Combine 12y and -5y to get 7y.

$$3y^{2}+7y-20-\left(y-3\right)\left(y-5\right)$$

Apply the distributive property by multiplying each term of y-3 by each term of y-5.

$$3y^{2}+7y-20-\left(y^{2}-5y-3y+15\right)$$

Combine -5y and -3y to get -8y.

$$3y^{2}+7y-20-\left(y^{2}-8y+15\right)$$

To find the opposite of y^{2}-8y+15, find the opposite of each term.

$$3y^{2}+7y-20-y^{2}-\left(-8y\right)-15$$

The opposite of -8y is 8y.

$$3y^{2}+7y-20-y^{2}+8y-15$$

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

$$2y^{2}+7y-20+8y-15$$

Combine 7y and 8y to get 15y.

$$2y^{2}+15y-20-15$$

Subtract 15 from -20 to get -35.

$$2y^{2}+15y-35$$