Solve y(y-4)-yleft(3-2yright)

$$y(y-4)-y \left( 3-2y \right)$$

Evaluate

$$y\left(3y-7\right)$$

Solution Steps

Use the distributive property to multiply y by y-4.

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

Use the distributive property to multiply y by 3-2y.

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

To find the opposite of 3y-2y^{2}, find the opposite of each term.

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

The opposite of -2y^{2} is 2y^{2}.

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

Combine -4y and -3y to get -7y.

$$y^{2}-7y+2y^{2}$$

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

$$3y^{2}-7y$$

Expand

$$3y^{2}-7y$$

Solution Steps

Use the distributive property to multiply y by y-4.

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

Use the distributive property to multiply y by 3-2y.

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

To find the opposite of 3y-2y^{2}, find the opposite of each term.

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

The opposite of -2y^{2} is 2y^{2}.

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

Combine -4y and -3y to get -7y.

$$y^{2}-7y+2y^{2}$$

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

$$3y^{2}-7y$$