Solve (n+5)^2-(n+3)^2

$$( n + 5 ) ^ { 2 } - ( n + 3 ) ^ { 2 }$$

Evaluate

$$4\left(n+4\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(n+5\right)^{2}.

$$n^{2}+10n+25-\left(n+3\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(n+3\right)^{2}.

$$n^{2}+10n+25-\left(n^{2}+6n+9\right)$$

To find the opposite of n^{2}+6n+9, find the opposite of each term.

$$n^{2}+10n+25-n^{2}-6n-9$$

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

$$10n+25-6n-9$$

Combine 10n and -6n to get 4n.

$$4n+25-9$$

Subtract 9 from 25 to get 16.

$$4n+16$$

Expand

$$4n+16$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(n+5\right)^{2}.

$$n^{2}+10n+25-\left(n+3\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(n+3\right)^{2}.

$$n^{2}+10n+25-\left(n^{2}+6n+9\right)$$

To find the opposite of n^{2}+6n+9, find the opposite of each term.

$$n^{2}+10n+25-n^{2}-6n-9$$

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

$$10n+25-6n-9$$

Combine 10n and -6n to get 4n.

$$4n+25-9$$

Subtract 9 from 25 to get 16.

$$4n+16$$