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

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

Evaluate

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

Solution Steps

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

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

Combine -2ab and ba to get -ab.

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

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

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

Combine 2ab and -ba to get ab.

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

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

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

Combine -ab and ab to get 0.

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

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

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

Expand

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

Solution Steps

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

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

Combine -2ab and ba to get -ab.

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

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

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

Combine 2ab and -ba to get ab.

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

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

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

Combine -ab and ab to get 0.

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

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

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