Solve (a-3b)(a+2b)-(a+5b)(a+3b)

$$( a - 3 b ) ( a + 2 b ) - ( a + 5 b ) ( a + 3 b )$$

Evaluate

$$-3b\left(3a+7b\right)$$

Solution Steps

Apply the distributive property by multiplying each term of a-3b by each term of a+2b.

$$a^{2}+2ab-3ba-6b^{2}-\left(a+5b\right)\left(a+3b\right)$$

Combine 2ab and -3ba to get -ab.

$$a^{2}-ab-6b^{2}-\left(a+5b\right)\left(a+3b\right)$$

Apply the distributive property by multiplying each term of a+5b by each term of a+3b.

$$a^{2}-ab-6b^{2}-\left(a^{2}+3ab+5ba+15b^{2}\right)$$

Combine 3ab and 5ba to get 8ab.

$$a^{2}-ab-6b^{2}-\left(a^{2}+8ab+15b^{2}\right)$$

To find the opposite of a^{2}+8ab+15b^{2}, find the opposite of each term.

$$a^{2}-ab-6b^{2}-a^{2}-8ab-15b^{2}$$

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

$$-ab-6b^{2}-8ab-15b^{2}$$

Combine -ab and -8ab to get -9ab.

$$-9ab-6b^{2}-15b^{2}$$

Combine -6b^{2} and -15b^{2} to get -21b^{2}.

$$-9ab-21b^{2}$$

Expand

$$-9ab-21b^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of a-3b by each term of a+2b.

$$a^{2}+2ab-3ba-6b^{2}-\left(a+5b\right)\left(a+3b\right)$$

Combine 2ab and -3ba to get -ab.

$$a^{2}-ab-6b^{2}-\left(a+5b\right)\left(a+3b\right)$$

Apply the distributive property by multiplying each term of a+5b by each term of a+3b.

$$a^{2}-ab-6b^{2}-\left(a^{2}+3ab+5ba+15b^{2}\right)$$

Combine 3ab and 5ba to get 8ab.

$$a^{2}-ab-6b^{2}-\left(a^{2}+8ab+15b^{2}\right)$$

To find the opposite of a^{2}+8ab+15b^{2}, find the opposite of each term.

$$a^{2}-ab-6b^{2}-a^{2}-8ab-15b^{2}$$

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

$$-ab-6b^{2}-8ab-15b^{2}$$

Combine -ab and -8ab to get -9ab.

$$-9ab-6b^{2}-15b^{2}$$

Combine -6b^{2} and -15b^{2} to get -21b^{2}.

$$-9ab-21b^{2}$$