Solve (4a-b)(2a-3b)-(-a+b)(3b-2a)

$$( 4 a - b ) ( 2 a - 3 b ) - ( - a + b ) ( 3 b - 2 a )$$

Evaluate

$$3a\left(2a-3b\right)$$

Solution Steps

Apply the distributive property by multiplying each term of 4a-b by each term of 2a-3b.

$$8a^{2}-12ab-2ba+3b^{2}-\left(-a+b\right)\left(3b-2a\right)$$

Combine -12ab and -2ba to get -14ab.

$$8a^{2}-14ab+3b^{2}-\left(-a+b\right)\left(3b-2a\right)$$

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

$$8a^{2}-14ab+3b^{2}-\left(3\left(-a\right)b-2\left(-a\right)a+3b^{2}-2ba\right)$$

Multiply -2 and -1 to get 2.

$$8a^{2}-14ab+3b^{2}-\left(3\left(-a\right)b+2aa+3b^{2}-2ba\right)$$

Multiply a and a to get a^{2}.

$$8a^{2}-14ab+3b^{2}-\left(3\left(-a\right)b+2a^{2}+3b^{2}-2ba\right)$$

To find the opposite of 3\left(-a\right)b+2a^{2}+3b^{2}-2ba, find the opposite of each term.

$$8a^{2}-14ab+3b^{2}-3\left(-a\right)b-2a^{2}-3b^{2}-\left(-2ba\right)$$

Multiply -3 and -1 to get 3.

$$8a^{2}-14ab+3b^{2}+3ab-2a^{2}-3b^{2}-\left(-2ba\right)$$

Combine -14ab and 3ab to get -11ab.

$$8a^{2}-11ab+3b^{2}-2a^{2}-3b^{2}-\left(-2ba\right)$$

Combine 8a^{2} and -2a^{2} to get 6a^{2}.

$$6a^{2}-11ab+3b^{2}-3b^{2}-\left(-2ba\right)$$

Combine 3b^{2} and -3b^{2} to get 0.

$$6a^{2}-11ab-\left(-2ba\right)$$

The opposite of -2ba is 2ba.

$$6a^{2}-11ab+2ba$$

Combine -11ab and 2ba to get -9ab.

$$6a^{2}-9ab$$

Expand

$$6a^{2}-9ab$$

Solution Steps

Apply the distributive property by multiplying each term of 4a-b by each term of 2a-3b.

$$8a^{2}-12ab-2ba+3b^{2}-\left(-a+b\right)\left(3b-2a\right)$$

Combine -12ab and -2ba to get -14ab.

$$8a^{2}-14ab+3b^{2}-\left(-a+b\right)\left(3b-2a\right)$$

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

$$8a^{2}-14ab+3b^{2}-\left(3\left(-a\right)b-2\left(-a\right)a+3b^{2}-2ba\right)$$

Multiply -2 and -1 to get 2.

$$8a^{2}-14ab+3b^{2}-\left(3\left(-a\right)b+2aa+3b^{2}-2ba\right)$$

Multiply a and a to get a^{2}.

$$8a^{2}-14ab+3b^{2}-\left(3\left(-a\right)b+2a^{2}+3b^{2}-2ba\right)$$

To find the opposite of 3\left(-a\right)b+2a^{2}+3b^{2}-2ba, find the opposite of each term.

$$8a^{2}-14ab+3b^{2}-3\left(-a\right)b-2a^{2}-3b^{2}-\left(-2ba\right)$$

Multiply -3 and -1 to get 3.

$$8a^{2}-14ab+3b^{2}+3ab-2a^{2}-3b^{2}-\left(-2ba\right)$$

Combine -14ab and 3ab to get -11ab.

$$8a^{2}-11ab+3b^{2}-2a^{2}-3b^{2}-\left(-2ba\right)$$

Combine 8a^{2} and -2a^{2} to get 6a^{2}.

$$6a^{2}-11ab+3b^{2}-3b^{2}-\left(-2ba\right)$$

Combine 3b^{2} and -3b^{2} to get 0.

$$6a^{2}-11ab-\left(-2ba\right)$$

The opposite of -2ba is 2ba.

$$6a^{2}-11ab+2ba$$

Combine -11ab and 2ba to get -9ab.

$$6a^{2}-9ab$$