Solve 2{p+q-3[p(p-2q)-q(q-2p)]}

$$2 \{ p + q - 3 [ p ( p - 2 q ) - q ( q - 2 p ) ] \}$$

Evaluate

$$-2\left(3p-3q-1\right)\left(p+q\right)$$

Solution Steps

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

$$2\left(p+q-3\left(p^{2}-2pq-q\left(q-2p\right)\right)\right)$$

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

$$2\left(p+q-3\left(p^{2}-2pq-\left(q^{2}-2qp\right)\right)\right)$$

To find the opposite of q^{2}-2qp, find the opposite of each term.

$$2\left(p+q-3\left(p^{2}-2pq-q^{2}-\left(-2qp\right)\right)\right)$$

The opposite of -2qp is 2qp.

$$2\left(p+q-3\left(p^{2}-2pq-q^{2}+2qp\right)\right)$$

Combine -2pq and 2qp to get 0.

$$2\left(p+q-3\left(p^{2}-q^{2}\right)\right)$$

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

$$2\left(p+q-3p^{2}+3q^{2}\right)$$

Use the distributive property to multiply 2 by p+q-3p^{2}+3q^{2}.

$$2p+2q-6p^{2}+6q^{2}$$

Expand

$$2q+6q^{2}+2p-6p^{2}$$

Solution Steps

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

$$2\left(p+q-3\left(p^{2}-2pq-q\left(q-2p\right)\right)\right)$$

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

$$2\left(p+q-3\left(p^{2}-2pq-\left(q^{2}-2qp\right)\right)\right)$$

To find the opposite of q^{2}-2qp, find the opposite of each term.

$$2\left(p+q-3\left(p^{2}-2pq-q^{2}-\left(-2qp\right)\right)\right)$$

The opposite of -2qp is 2qp.

$$2\left(p+q-3\left(p^{2}-2pq-q^{2}+2qp\right)\right)$$

Combine -2pq and 2qp to get 0.

$$2\left(p+q-3\left(p^{2}-q^{2}\right)\right)$$

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

$$2\left(p+q-3p^{2}+3q^{2}\right)$$

Use the distributive property to multiply 2 by p+q-3p^{2}+3q^{2}.

$$2p+2q-6p^{2}+6q^{2}$$