Solve left(6z+7yright)left(3z+4yright)-left(4z-6zright)left(4z+6zright)

$$\left( 6z+7y \right) \left( 3z+4y \right) - \left( 4z-6z \right) \left( 4z+6z \right)$$

Evaluate

$$28y^{2}+45yz+38z^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 6z+7y by each term of 3z+4y.

$$18z^{2}+24zy+21yz+28y^{2}-\left(4z-6z\right)\left(4z+6z\right)$$

Combine 24zy and 21yz to get 45zy.

$$18z^{2}+45zy+28y^{2}-\left(4z-6z\right)\left(4z+6z\right)$$

Combine 4z and -6z to get -2z.

$$18z^{2}+45zy+28y^{2}-\left(-2z\left(4z+6z\right)\right)$$

Combine 4z and 6z to get 10z.

$$18z^{2}+45zy+28y^{2}-\left(-2z\times 10z\right)$$

Multiply -2 and 10 to get -20.

$$18z^{2}+45zy+28y^{2}-\left(-20zz\right)$$

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

$$18z^{2}+45zy+28y^{2}-\left(-20z^{2}\right)$$

The opposite of -20z^{2} is 20z^{2}.

$$18z^{2}+45zy+28y^{2}+20z^{2}$$

Combine 18z^{2} and 20z^{2} to get 38z^{2}.

$$38z^{2}+45zy+28y^{2}$$

Expand

$$28y^{2}+45yz+38z^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 6z+7y by each term of 3z+4y.

$$18z^{2}+24zy+21yz+28y^{2}-\left(4z-6z\right)\left(4z+6z\right)$$

Combine 24zy and 21yz to get 45zy.

$$18z^{2}+45zy+28y^{2}-\left(4z-6z\right)\left(4z+6z\right)$$

Combine 4z and -6z to get -2z.

$$18z^{2}+45zy+28y^{2}-\left(-2z\left(4z+6z\right)\right)$$

Combine 4z and 6z to get 10z.

$$18z^{2}+45zy+28y^{2}-\left(-2z\times 10z\right)$$

Multiply -2 and 10 to get -20.

$$18z^{2}+45zy+28y^{2}-\left(-20zz\right)$$

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

$$18z^{2}+45zy+28y^{2}-\left(-20z^{2}\right)$$

The opposite of -20z^{2} is 20z^{2}.

$$18z^{2}+45zy+28y^{2}+20z^{2}$$

Combine 18z^{2} and 20z^{2} to get 38z^{2}.

$$38z^{2}+45zy+28y^{2}$$