# How do you find g(5n) given g(x)=x^2-x?

Jan 18, 2017

$g \left(5 n\right) = 25 {n}^{2} - 5 n$

#### Explanation:

Simply replace the $x$ in the function's formula with whatever you see in the parentheses to evaluate $g$ at that point. We get:

$g \left(5 n\right) = {\left(5 n\right)}^{2} - 5 n$

Recall that ${\left(a b\right)}^{2} = {a}^{2} {b}^{2}$, so:

$g \left(5 n\right) = 25 \cdot {n}^{2} - 5 n$

The tricky part here is that parentheses like ${\left(5 n\right)}^{2}$ are often omitted (which is obviously a mistake) and are often interpreted like $5 {n}^{2}$, which just means $5$ times ${n}^{2}$, or $25 n$, which means ${5}^{2} \cdot n$ (again, those are just common mistakes). However, the correct way is to always use them when substituting a "bigger" term in place of a smaller one, for example when using $a b c$ instead of $d$ in the formula ${d}^{3}$, the correct substitution is ${\left(a b c\right)}^{3} = {a}^{3} {b}^{3} {c}^{3}$, and none other.