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

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

Evaluate

$$4a^{2}-2ab-4b^{2}$$

Solution Steps

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

$$6a^{2}+4ab-9ba-6b^{2}-\left(2a+b\right)\left(a-2b\right)$$

Combine 4ab and -9ba to get -5ab.

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

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

$$6a^{2}-5ab-6b^{2}-\left(2a^{2}-4ab+ba-2b^{2}\right)$$

Combine -4ab and ba to get -3ab.

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

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

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

The opposite of -3ab is 3ab.

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

The opposite of -2b^{2} is 2b^{2}.

$$6a^{2}-5ab-6b^{2}-2a^{2}+3ab+2b^{2}$$

Combine 6a^{2} and -2a^{2} to get 4a^{2}.

$$4a^{2}-5ab-6b^{2}+3ab+2b^{2}$$

Combine -5ab and 3ab to get -2ab.

$$4a^{2}-2ab-6b^{2}+2b^{2}$$

Combine -6b^{2} and 2b^{2} to get -4b^{2}.

$$4a^{2}-2ab-4b^{2}$$

Expand

$$4a^{2}-2ab-4b^{2}$$

Solution Steps

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

$$6a^{2}+4ab-9ba-6b^{2}-\left(2a+b\right)\left(a-2b\right)$$

Combine 4ab and -9ba to get -5ab.

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

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

$$6a^{2}-5ab-6b^{2}-\left(2a^{2}-4ab+ba-2b^{2}\right)$$

Combine -4ab and ba to get -3ab.

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

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

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

The opposite of -3ab is 3ab.

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

The opposite of -2b^{2} is 2b^{2}.

$$6a^{2}-5ab-6b^{2}-2a^{2}+3ab+2b^{2}$$

Combine 6a^{2} and -2a^{2} to get 4a^{2}.

$$4a^{2}-5ab-6b^{2}+3ab+2b^{2}$$

Combine -5ab and 3ab to get -2ab.

$$4a^{2}-2ab-6b^{2}+2b^{2}$$

Combine -6b^{2} and 2b^{2} to get -4b^{2}.

$$4a^{2}-2ab-4b^{2}$$