Algebra Examples

$f (x) = x + 5$ , $g (x) = x^{3} + 125$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (x + 5)$ by substituting in the value of $f$ into $g$ .

$g (x + 5) = {(x + 5)}^{3} + 125$

Step 3

Simplify each term.

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Step 3.1

Use the Binomial Theorem.

$g (x + 5) = x^{3} + 3 x^{2} \cdot 5 + 3 x \cdot 5^{2} + 5^{3} + 125$

Step 3.2

Simplify each term.

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Step 3.2.1

Multiply $5$ by $3$ .

$g (x + 5) = x^{3} + 15 x^{2} + 3 x \cdot 5^{2} + 5^{3} + 125$

Step 3.2.2

Raise $5$ to the power of $2$ .

$g (x + 5) = x^{3} + 15 x^{2} + 3 x \cdot 25 + 5^{3} + 125$

Step 3.2.3

Multiply $25$ by $3$ .

$g (x + 5) = x^{3} + 15 x^{2} + 75 x + 5^{3} + 125$

Step 3.2.4

Raise $5$ to the power of $3$ .

$g (x + 5) = x^{3} + 15 x^{2} + 75 x + 125 + 125$

Step 4

Add $125$ and $125$ .

$g (x + 5) = x^{3} + 15 x^{2} + 75 x + 250$