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

$$( a + b ) ^ { 2 } - b ( 2 a + b )$$

Evaluate

$$a^{2}$$

Solution Steps

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

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

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

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

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

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

Combine 2ab and -2ba to get 0.

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

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

$$a^{2}$$

Expand

$$a^{2}$$

Solution Steps

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

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

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

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

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

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

Combine 2ab and -2ba to get 0.

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

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

$$a^{2}$$