Solve (8)(2p+q)(2p-q)

$$( 8 ) ( 2 p + q ) ( 2 p - q )$$

Evaluate

$$32p^{2}-8q^{2}$$

Solution Steps

Use the distributive property to multiply 8 by 2p+q.

$$\left(16p+8q\right)\left(2p-q\right)$$

Apply the distributive property by multiplying each term of 16p+8q by each term of 2p-q.

$$32p^{2}-16pq+16qp-8q^{2}$$

Combine -16pq and 16qp to get 0.

$$32p^{2}-8q^{2}$$

Expand

$$32p^{2}-8q^{2}$$

Solution Steps

Use the distributive property to multiply 8 by 2p+q.

$$\left(16p+8q\right)\left(2p-q\right)$$

Apply the distributive property by multiplying each term of 16p+8q by each term of 2p-q.

$$32p^{2}-16pq+16qp-8q^{2}$$

Combine -16pq and 16qp to get 0.

$$32p^{2}-8q^{2}$$