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

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

Evaluate

$$4ab$$

Solution Steps

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

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

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

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

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

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

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

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

Combine 2ab and 2ab to get 4ab.

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

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

$$4ab$$

Expand

$$4ab$$

Solution Steps

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

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

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

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

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

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

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

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

Combine 2ab and 2ab to get 4ab.

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

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

$$4ab$$