Solve (3p-9)(2p-9)+(3p-9)(p-2p)=

$$( 3 p - 9 ) ( 2 p - 9 ) + ( 3 p - 9 ) ( p - 2 p ) =$$

Evaluate

$$3\left(p-9\right)\left(p-3\right)$$

Solution Steps

Apply the distributive property by multiplying each term of 3p-9 by each term of 2p-9.

$$6p^{2}-27p-18p+81+\left(3p-9\right)\left(p-2p\right)$$

Combine -27p and -18p to get -45p.

$$6p^{2}-45p+81+\left(3p-9\right)\left(p-2p\right)$$

Combine p and -2p to get -p.

$$6p^{2}-45p+81+\left(3p-9\right)\left(-1\right)p$$

Use the distributive property to multiply 3p-9 by -1.

$$6p^{2}-45p+81+\left(-3p+9\right)p$$

Use the distributive property to multiply -3p+9 by p.

$$6p^{2}-45p+81-3p^{2}+9p$$

Combine 6p^{2} and -3p^{2} to get 3p^{2}.

$$3p^{2}-45p+81+9p$$

Combine -45p and 9p to get -36p.

$$3p^{2}-36p+81$$

Expand

$$3p^{2}-36p+81$$

Solution Steps

Apply the distributive property by multiplying each term of 3p-9 by each term of 2p-9.

$$6p^{2}-27p-18p+81+\left(3p-9\right)\left(p-2p\right)$$

Combine -27p and -18p to get -45p.

$$6p^{2}-45p+81+\left(3p-9\right)\left(p-2p\right)$$

Combine p and -2p to get -p.

$$6p^{2}-45p+81+\left(3p-9\right)\left(-1\right)p$$

Use the distributive property to multiply 3p-9 by -1.

$$6p^{2}-45p+81+\left(-3p+9\right)p$$

Use the distributive property to multiply -3p+9 by p.

$$6p^{2}-45p+81-3p^{2}+9p$$

Combine 6p^{2} and -3p^{2} to get 3p^{2}.

$$3p^{2}-45p+81+9p$$

Combine -45p and 9p to get -36p.

$$3p^{2}-36p+81$$