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

$$( 2 a + b ) \cdot ( a + 2 b ) - ( a - b ) \cdot ( 2 a - 2 b )$$

Evaluate

$$9ab$$

Solution Steps

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

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

Combine 4ab and ba to get 5ab.

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

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

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

Combine -2ab and -2ba to get -4ab.

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

To find the opposite of 2a^{2}-4ab+2b^{2}, find the opposite of each term.

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

The opposite of -4ab is 4ab.

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

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

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

Combine 5ab and 4ab to get 9ab.

$$9ab+2b^{2}-2b^{2}$$

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

$$9ab$$

Expand

$$9ab$$

Solution Steps

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

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

Combine 4ab and ba to get 5ab.

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

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

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

Combine -2ab and -2ba to get -4ab.

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

To find the opposite of 2a^{2}-4ab+2b^{2}, find the opposite of each term.

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

The opposite of -4ab is 4ab.

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

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

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

Combine 5ab and 4ab to get 9ab.

$$9ab+2b^{2}-2b^{2}$$

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

$$9ab$$