Solve (3y+2)(y-4)-(y-2)(y-3)

$$( 3 y + 2 ) ( y - 4 ) - ( y - 2 ) ( y - 3 )$$

Evaluate

$$2y^{2}-5y-14$$

Solution Steps

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

$$3y^{2}-12y+2y-8-\left(y-2\right)\left(y-3\right)$$

Combine -12y and 2y to get -10y.

$$3y^{2}-10y-8-\left(y-2\right)\left(y-3\right)$$

Apply the distributive property by multiplying each term of y-2 by each term of y-3.

$$3y^{2}-10y-8-\left(y^{2}-3y-2y+6\right)$$

Combine -3y and -2y to get -5y.

$$3y^{2}-10y-8-\left(y^{2}-5y+6\right)$$

To find the opposite of y^{2}-5y+6, find the opposite of each term.

$$3y^{2}-10y-8-y^{2}-\left(-5y\right)-6$$

The opposite of -5y is 5y.

$$3y^{2}-10y-8-y^{2}+5y-6$$

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

$$2y^{2}-10y-8+5y-6$$

Combine -10y and 5y to get -5y.

$$2y^{2}-5y-8-6$$

Subtract 6 from -8 to get -14.

$$2y^{2}-5y-14$$

Expand

$$2y^{2}-5y-14$$

Solution Steps

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

$$3y^{2}-12y+2y-8-\left(y-2\right)\left(y-3\right)$$

Combine -12y and 2y to get -10y.

$$3y^{2}-10y-8-\left(y-2\right)\left(y-3\right)$$

Apply the distributive property by multiplying each term of y-2 by each term of y-3.

$$3y^{2}-10y-8-\left(y^{2}-3y-2y+6\right)$$

Combine -3y and -2y to get -5y.

$$3y^{2}-10y-8-\left(y^{2}-5y+6\right)$$

To find the opposite of y^{2}-5y+6, find the opposite of each term.

$$3y^{2}-10y-8-y^{2}-\left(-5y\right)-6$$

The opposite of -5y is 5y.

$$3y^{2}-10y-8-y^{2}+5y-6$$

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

$$2y^{2}-10y-8+5y-6$$

Combine -10y and 5y to get -5y.

$$2y^{2}-5y-8-6$$

Subtract 6 from -8 to get -14.

$$2y^{2}-5y-14$$