Algebra Examples

$f (x) = 5 x^{3}$ , $g (x) = x + 1$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (x + 1)$ by substituting in the value of $g$ into $f$ .

$f (x + 1) = 5 {(x + 1)}^{3}$

Step 3

Use the Binomial Theorem.

$f (x + 1) = 5 (x^{3} + 3 x^{2} \cdot 1 + 3 x \cdot 1^{2} + 1^{3})$

Step 4

Simplify terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $3$ by $1$ .

$f (x + 1) = 5 (x^{3} + 3 x^{2} + 3 x \cdot 1^{2} + 1^{3})$

Step 4.1.2

One to any power is one.

$f (x + 1) = 5 (x^{3} + 3 x^{2} + 3 x \cdot 1 + 1^{3})$

Step 4.1.3

Multiply $3$ by $1$ .

$f (x + 1) = 5 (x^{3} + 3 x^{2} + 3 x + 1^{3})$

Step 4.1.4

One to any power is one.

$f (x + 1) = 5 (x^{3} + 3 x^{2} + 3 x + 1)$

Step 4.2

Apply the distributive property.

$f (x + 1) = 5 x^{3} + 5 (3 x^{2}) + 5 (3 x) + 5 \cdot 1$

Step 5

Simplify.

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Step 5.1

Multiply $3$ by $5$ .

$f (x + 1) = 5 x^{3} + 15 x^{2} + 5 (3 x) + 5 \cdot 1$

Step 5.2

Multiply $3$ by $5$ .

$f (x + 1) = 5 x^{3} + 15 x^{2} + 15 x + 5 \cdot 1$

Step 5.3

Multiply $5$ by $1$ .

$f (x + 1) = 5 x^{3} + 15 x^{2} + 15 x + 5$