Algebra Examples

$f (x) = x^{2} - 4$ , $g (x) = x^{3}$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (x^{2} - 4)$ by substituting in the value of $f$ into $g$ .

$g (x^{2} - 4) = {(x^{2} - 4)}^{3}$

Step 3

Use the Binomial Theorem.

$g (x^{2} - 4) = {(x^{2})}^{3} + 3 {(x^{2})}^{2} \cdot - 4 + 3 x^{2} {(- 4)}^{2} + {(- 4)}^{3}$

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

Multiply the exponents in ${(x^{2})}^{3}$ .

Tap for more steps...

Step 4.1.1

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

$g (x^{2} - 4) = x^{2 \cdot 3} + 3 {(x^{2})}^{2} \cdot - 4 + 3 x^{2} {(- 4)}^{2} + {(- 4)}^{3}$

Step 4.1.2

Multiply $2$ by $3$ .

$g (x^{2} - 4) = x^{6} + 3 {(x^{2})}^{2} \cdot - 4 + 3 x^{2} {(- 4)}^{2} + {(- 4)}^{3}$

Step 4.2

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

Tap for more steps...

Step 4.2.1

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

$g (x^{2} - 4) = x^{6} + 3 x^{2 \cdot 2} \cdot - 4 + 3 x^{2} {(- 4)}^{2} + {(- 4)}^{3}$

Step 4.2.2

Multiply $2$ by $2$ .

$g (x^{2} - 4) = x^{6} + 3 x^{4} \cdot - 4 + 3 x^{2} {(- 4)}^{2} + {(- 4)}^{3}$

Step 4.3

Multiply $- 4$ by $3$ .

$g (x^{2} - 4) = x^{6} - 12 x^{4} + 3 x^{2} {(- 4)}^{2} + {(- 4)}^{3}$

Step 4.4

Raise $- 4$ to the power of $2$ .

$g (x^{2} - 4) = x^{6} - 12 x^{4} + 3 x^{2} \cdot 16 + {(- 4)}^{3}$

Step 4.5

Multiply $16$ by $3$ .

$g (x^{2} - 4) = x^{6} - 12 x^{4} + 48 x^{2} + {(- 4)}^{3}$

Step 4.6

Raise $- 4$ to the power of $3$ .

$g (x^{2} - 4) = x^{6} - 12 x^{4} + 48 x^{2} - 64$