Solve (3a-b)(a-2b)-b(a+2b)-a]div2a

$$( 3 a - b ) ( a - 2 b ) - b ( a + 2 b ) - a ] \div 2 a$$

Evaluate

$$a\left(3a-8b-1\right)$$

Solution Steps

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

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

Combine -6ab and -ba to get -7ab.

$$3a^{2}-7ab+2b^{2}-b\left(a+2b\right)-a$$

Use the distributive property to multiply b by a+2b.

$$3a^{2}-7ab+2b^{2}-\left(ba+2b^{2}\right)-a$$

To find the opposite of ba+2b^{2}, find the opposite of each term.

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

Combine -7ab and -ba to get -8ab.

$$3a^{2}-8ab+2b^{2}-2b^{2}-a$$

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

$$3a^{2}-8ab-a$$

Expand

$$3a^{2}-8ab-a$$

Solution Steps

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

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

Combine -6ab and -ba to get -7ab.

$$3a^{2}-7ab+2b^{2}-b\left(a+2b\right)-a$$

Use the distributive property to multiply b by a+2b.

$$3a^{2}-7ab+2b^{2}-\left(ba+2b^{2}\right)-a$$

To find the opposite of ba+2b^{2}, find the opposite of each term.

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

Combine -7ab and -ba to get -8ab.

$$3a^{2}-8ab+2b^{2}-2b^{2}-a$$

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

$$3a^{2}-8ab-a$$