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

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

Evaluate

$$4ak$$

Solution Steps

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

$$a^{2}+2ak+k^{2}-\left(a-k\right)^{2}$$

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

$$a^{2}+2ak+k^{2}-\left(a^{2}-2ak+k^{2}\right)$$

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

$$a^{2}+2ak+k^{2}-a^{2}+2ak-k^{2}$$

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

$$2ak+k^{2}+2ak-k^{2}$$

Combine 2ak and 2ak to get 4ak.

$$4ak+k^{2}-k^{2}$$

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

$$4ak$$

Expand

$$4ak$$

Solution Steps

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

$$a^{2}+2ak+k^{2}-\left(a-k\right)^{2}$$

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

$$a^{2}+2ak+k^{2}-\left(a^{2}-2ak+k^{2}\right)$$

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

$$a^{2}+2ak+k^{2}-a^{2}+2ak-k^{2}$$

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

$$2ak+k^{2}+2ak-k^{2}$$

Combine 2ak and 2ak to get 4ak.

$$4ak+k^{2}-k^{2}$$

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

$$4ak$$