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

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

Evaluate

$$\left(a-2b\right)\left(3a-b\right)$$

Solution Steps

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

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

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

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

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

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

Combine 2ab and 2ba to get 4ab.

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

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

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

The opposite of -a^{2} is a^{2}.

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

The opposite of -4b^{2} is 4b^{2}.

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

Combine -3ab and -4ab to get -7ab.

$$-7ab+2a^{2}-2b^{2}+a^{2}+4b^{2}$$

Combine 2a^{2} and a^{2} to get 3a^{2}.

$$-7ab+3a^{2}-2b^{2}+4b^{2}$$

Combine -2b^{2} and 4b^{2} to get 2b^{2}.

$$-7ab+3a^{2}+2b^{2}$$

Expand

$$3a^{2}-7ab+2b^{2}$$

Solution Steps

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

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

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

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

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

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

Combine 2ab and 2ba to get 4ab.

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

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

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

The opposite of -a^{2} is a^{2}.

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

The opposite of -4b^{2} is 4b^{2}.

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

Combine -3ab and -4ab to get -7ab.

$$-7ab+2a^{2}-2b^{2}+a^{2}+4b^{2}$$

Combine 2a^{2} and a^{2} to get 3a^{2}.

$$-7ab+3a^{2}-2b^{2}+4b^{2}$$

Combine -2b^{2} and 4b^{2} to get 2b^{2}.

$$-7ab+3a^{2}+2b^{2}$$