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

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

Evaluate

$$5b\left(2a+b\right)$$

Solution Steps

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

$$2a^{2}+4ab+ba+2b^{2}-\left(a-3b\right)\left(2a+b\right)$$

Combine 4ab and ba to get 5ab.

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

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

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

Combine ab and -6ba to get -5ab.

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

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

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

The opposite of -5ab is 5ab.

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

The opposite of -3b^{2} is 3b^{2}.

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

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

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

Combine 5ab and 5ab to get 10ab.

$$10ab+2b^{2}+3b^{2}$$

Combine 2b^{2} and 3b^{2} to get 5b^{2}.

$$10ab+5b^{2}$$

Expand

$$10ab+5b^{2}$$

Solution Steps

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

$$2a^{2}+4ab+ba+2b^{2}-\left(a-3b\right)\left(2a+b\right)$$

Combine 4ab and ba to get 5ab.

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

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

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

Combine ab and -6ba to get -5ab.

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

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

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

The opposite of -5ab is 5ab.

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

The opposite of -3b^{2} is 3b^{2}.

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

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

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

Combine 5ab and 5ab to get 10ab.

$$10ab+2b^{2}+3b^{2}$$

Combine 2b^{2} and 3b^{2} to get 5b^{2}.

$$10ab+5b^{2}$$