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

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

Evaluate

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

Solution Steps

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

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

Combine -ab and 2ba to get ab.

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

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

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

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

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

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

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

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

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

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

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

Expand

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

Solution Steps

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

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

Combine -ab and 2ba to get ab.

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

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

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

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

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

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

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

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

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

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

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