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

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

Evaluate

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

Solution Steps

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

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

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

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

Use the distributive property to multiply a by 5a-3b.

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

To find the opposite of 5a^{2}-3ab, find the opposite of each term.

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

The opposite of -3ab is 3ab.

$$3a^{2}-ab-2b^{2}-5a^{2}+3ab$$

Combine 3a^{2} and -5a^{2} to get -2a^{2}.

$$-2a^{2}-ab-2b^{2}+3ab$$

Combine -ab and 3ab to get 2ab.

$$-2a^{2}+2ab-2b^{2}$$

Expand

$$-2a^{2}+2ab-2b^{2}$$

Solution Steps

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

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

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

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

Use the distributive property to multiply a by 5a-3b.

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

To find the opposite of 5a^{2}-3ab, find the opposite of each term.

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

The opposite of -3ab is 3ab.

$$3a^{2}-ab-2b^{2}-5a^{2}+3ab$$

Combine 3a^{2} and -5a^{2} to get -2a^{2}.

$$-2a^{2}-ab-2b^{2}+3ab$$

Combine -ab and 3ab to get 2ab.

$$-2a^{2}+2ab-2b^{2}$$