Precalculus Examples

$f (n) = n^{2} - 2 n$ ; Find $f (n^{2})$

Step 1

Replace the variable $n$ with $n^{2}$ in the expression.

$f (n^{2}) = {(n^{2})}^{2} - 2 n^{2}$

Step 2

Simplify ${(n^{2})}^{2} - 2 n^{2}$ .

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Step 2.1

Remove parentheses.

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

Step 2.2

Multiply the exponents in ${(n^{2})}^{2}$ .

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Step 2.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$n^{2 \cdot 2} - 2 n^{2}$

Step 2.2.2

Multiply $2$ by $2$ .

$n^{4} - 2 n^{2}$