Solve (4p-3r)(p+2r)-(3p-r)(p+6r)=

$$( 4 p - 3 r ) ( p + 2 r ) - ( 3 p - r ) ( p + 6 r ) =$$

Evaluate

$$p\left(p-12r\right)$$

Solution Steps

Apply the distributive property by multiplying each term of 4p-3r by each term of p+2r.

$$4p^{2}+8pr-3rp-6r^{2}-\left(3p-r\right)\left(p+6r\right)$$

Combine 8pr and -3rp to get 5pr.

$$4p^{2}+5pr-6r^{2}-\left(3p-r\right)\left(p+6r\right)$$

Apply the distributive property by multiplying each term of 3p-r by each term of p+6r.

$$4p^{2}+5pr-6r^{2}-\left(3p^{2}+18pr-rp-6r^{2}\right)$$

Combine 18pr and -rp to get 17pr.

$$4p^{2}+5pr-6r^{2}-\left(3p^{2}+17pr-6r^{2}\right)$$

To find the opposite of 3p^{2}+17pr-6r^{2}, find the opposite of each term.

$$4p^{2}+5pr-6r^{2}-3p^{2}-17pr-\left(-6r^{2}\right)$$

The opposite of -6r^{2} is 6r^{2}.

$$4p^{2}+5pr-6r^{2}-3p^{2}-17pr+6r^{2}$$

Combine 4p^{2} and -3p^{2} to get p^{2}.

$$p^{2}+5pr-6r^{2}-17pr+6r^{2}$$

Combine 5pr and -17pr to get -12pr.

$$p^{2}-12pr-6r^{2}+6r^{2}$$

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

$$p^{2}-12pr$$

Expand

$$p^{2}-12pr$$

Solution Steps

Apply the distributive property by multiplying each term of 4p-3r by each term of p+2r.

$$4p^{2}+8pr-3rp-6r^{2}-\left(3p-r\right)\left(p+6r\right)$$

Combine 8pr and -3rp to get 5pr.

$$4p^{2}+5pr-6r^{2}-\left(3p-r\right)\left(p+6r\right)$$

Apply the distributive property by multiplying each term of 3p-r by each term of p+6r.

$$4p^{2}+5pr-6r^{2}-\left(3p^{2}+18pr-rp-6r^{2}\right)$$

Combine 18pr and -rp to get 17pr.

$$4p^{2}+5pr-6r^{2}-\left(3p^{2}+17pr-6r^{2}\right)$$

To find the opposite of 3p^{2}+17pr-6r^{2}, find the opposite of each term.

$$4p^{2}+5pr-6r^{2}-3p^{2}-17pr-\left(-6r^{2}\right)$$

The opposite of -6r^{2} is 6r^{2}.

$$4p^{2}+5pr-6r^{2}-3p^{2}-17pr+6r^{2}$$

Combine 4p^{2} and -3p^{2} to get p^{2}.

$$p^{2}+5pr-6r^{2}-17pr+6r^{2}$$

Combine 5pr and -17pr to get -12pr.

$$p^{2}-12pr-6r^{2}+6r^{2}$$

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

$$p^{2}-12pr$$