Solve (a+b)^2-b(2a+b)-8a]div2a

$$( a + b ) ^ { 2 } - b ( 2 a + b ) - 8 a ] \div 2 a$$

Evaluate

$$a\left(a-8\right)$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+b\right)^{2}.

$$a^{2}+2ab+b^{2}-b\left(2a+b\right)-8a$$

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

$$a^{2}+2ab+b^{2}-\left(2ba+b^{2}\right)-8a$$

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

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

Combine 2ab and -2ba to get 0.

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

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

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

Expand

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

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+b\right)^{2}.

$$a^{2}+2ab+b^{2}-b\left(2a+b\right)-8a$$

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

$$a^{2}+2ab+b^{2}-\left(2ba+b^{2}\right)-8a$$

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

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

Combine 2ab and -2ba to get 0.

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

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

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