Solve (n+x)^2-(n-x)^2

$$( n + x ) ^ { 2 } - ( n - x ) ^ { 2 }$$

Evaluate

$$4nx$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(n+x\right)^{2}.

$$n^{2}+2nx+x^{2}-\left(n-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(n-x\right)^{2}.

$$n^{2}+2nx+x^{2}-\left(n^{2}-2nx+x^{2}\right)$$

To find the opposite of n^{2}-2nx+x^{2}, find the opposite of each term.

$$n^{2}+2nx+x^{2}-n^{2}+2nx-x^{2}$$

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

$$2nx+x^{2}+2nx-x^{2}$$

Combine 2nx and 2nx to get 4nx.

$$4nx+x^{2}-x^{2}$$

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

$$4nx$$

Expand

$$4nx$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(n+x\right)^{2}.

$$n^{2}+2nx+x^{2}-\left(n-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(n-x\right)^{2}.

$$n^{2}+2nx+x^{2}-\left(n^{2}-2nx+x^{2}\right)$$

To find the opposite of n^{2}-2nx+x^{2}, find the opposite of each term.

$$n^{2}+2nx+x^{2}-n^{2}+2nx-x^{2}$$

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

$$2nx+x^{2}+2nx-x^{2}$$

Combine 2nx and 2nx to get 4nx.

$$4nx+x^{2}-x^{2}$$

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

$$4nx$$