Solve (3p-q)(2p-q)+(3p-q)(q-2p)=

$$( 3 p - q ) ( 2 p - q ) + ( 3 p - q ) ( q - 2 p ) =$$

Evaluate

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Solution Steps

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

$$6p^{2}-3pq-2qp+q^{2}+\left(3p-q\right)\left(q-2p\right)$$

Combine -3pq and -2qp to get -5pq.

$$6p^{2}-5pq+q^{2}+\left(3p-q\right)\left(q-2p\right)$$

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

$$6p^{2}-5pq+q^{2}+3pq-6p^{2}-q^{2}+2qp$$

Combine 3pq and 2qp to get 5pq.

$$6p^{2}-5pq+q^{2}+5pq-6p^{2}-q^{2}$$

Combine -5pq and 5pq to get 0.

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

Combine 6p^{2} and -6p^{2} to get 0.

$$q^{2}-q^{2}$$

Combine q^{2} and -q^{2} to get 0.

$$0$$

Factor

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Solution Steps

Factor out common term 3p-q by using distributive property.

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

Consider 2p-q+q-2p. Simplify.

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