Solve -2p+2(2p-q-3)(4p-3q-7)

$$- 2 p + 2 ( 2 p - q - 3 ) ( 4 p - 3 q - 7 )$$

Evaluate

$$2\left(\left(2p-q-3\right)\left(4p-3q-7\right)-p\right)$$

Solution Steps

Use the distributive property to multiply 2 by 2p-q-3.

$$-2p+\left(4p-2q-6\right)\left(4p-3q-7\right)$$

Apply the distributive property by multiplying each term of 4p-2q-6 by each term of 4p-3q-7.

$$-2p+16p^{2}-12pq-28p-8qp+6q^{2}+14q-24p+18q+42$$

Combine -12pq and -8qp to get -20pq.

$$-2p+16p^{2}-20pq-28p+6q^{2}+14q-24p+18q+42$$

Combine -28p and -24p to get -52p.

$$-2p+16p^{2}-20pq-52p+6q^{2}+14q+18q+42$$

Combine 14q and 18q to get 32q.

$$-2p+16p^{2}-20pq-52p+6q^{2}+32q+42$$

Combine -2p and -52p to get -54p.

$$-54p+16p^{2}-20pq+6q^{2}+32q+42$$

Expand

$$16p^{2}-20pq-54p+6q^{2}+32q+42$$

Solution Steps

Use the distributive property to multiply 2 by 2p-q-3.

$$-2p+\left(4p-2q-6\right)\left(4p-3q-7\right)$$

Apply the distributive property by multiplying each term of 4p-2q-6 by each term of 4p-3q-7.

$$-2p+16p^{2}-12pq-28p-8qp+6q^{2}+14q-24p+18q+42$$

Combine -12pq and -8qp to get -20pq.

$$-2p+16p^{2}-20pq-28p+6q^{2}+14q-24p+18q+42$$

Combine -28p and -24p to get -52p.

$$-2p+16p^{2}-20pq-52p+6q^{2}+14q+18q+42$$

Combine 14q and 18q to get 32q.

$$-2p+16p^{2}-20pq-52p+6q^{2}+32q+42$$

Combine -2p and -52p to get -54p.

$$-54p+16p^{2}-20pq+6q^{2}+32q+42$$