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

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

Evaluate

$$2a\left(2a+b\right)$$

Solution Steps

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

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

Combine 3ab and 2ba to get 5ab.

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

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

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

Combine ab and 2ba to get 3ab.

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

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

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

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

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

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

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

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

$$4a^{2}+2ab$$

Expand

$$4a^{2}+2ab$$

Solution Steps

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

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

Combine 3ab and 2ba to get 5ab.

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

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

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

Combine ab and 2ba to get 3ab.

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

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

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

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

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

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

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

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

$$4a^{2}+2ab$$