Precalculus Examples

$(1 + x^{\frac{4}{3}}) (1 - x^{\frac{2}{3}})$

Step 1

Expand $(1 + x^{\frac{4}{3}}) (1 - x^{\frac{2}{3}})$ using the FOIL Method.

Tap for more steps...

Step 1.1

Apply the distributive property.

$1 (1 - x^{\frac{2}{3}}) + x^{\frac{4}{3}} (1 - x^{\frac{2}{3}})$

Step 1.2

Apply the distributive property.

$1 \cdot 1 + 1 (- x^{\frac{2}{3}}) + x^{\frac{4}{3}} (1 - x^{\frac{2}{3}})$

Step 1.3

Apply the distributive property.

$1 \cdot 1 + 1 (- x^{\frac{2}{3}}) + x^{\frac{4}{3}} \cdot 1 + x^{\frac{4}{3}} (- x^{\frac{2}{3}})$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Multiply $1$ by $1$ .

$1 + 1 (- x^{\frac{2}{3}}) + x^{\frac{4}{3}} \cdot 1 + x^{\frac{4}{3}} (- x^{\frac{2}{3}})$

Step 2.2

Multiply $- x^{\frac{2}{3}}$ by $1$ .

$1 - x^{\frac{2}{3}} + x^{\frac{4}{3}} \cdot 1 + x^{\frac{4}{3}} (- x^{\frac{2}{3}})$

Step 2.3

Multiply $x^{\frac{4}{3}}$ by $1$ .

$1 - x^{\frac{2}{3}} + x^{\frac{4}{3}} + x^{\frac{4}{3}} (- x^{\frac{2}{3}})$

Step 2.4

Rewrite using the commutative property of multiplication.

$1 - x^{\frac{2}{3}} + x^{\frac{4}{3}} - x^{\frac{4}{3}} x^{\frac{2}{3}}$

Step 2.5

Multiply $x^{\frac{4}{3}}$ by $x^{\frac{2}{3}}$ by adding the exponents.

Tap for more steps...

Step 2.5.1

Move $x^{\frac{2}{3}}$ .

$1 - x^{\frac{2}{3}} + x^{\frac{4}{3}} - (x^{\frac{2}{3}} x^{\frac{4}{3}})$

Step 2.5.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$1 - x^{\frac{2}{3}} + x^{\frac{4}{3}} - x^{\frac{2}{3} + \frac{4}{3}}$

Step 2.5.3

Combine the numerators over the common denominator.

$1 - x^{\frac{2}{3}} + x^{\frac{4}{3}} - x^{\frac{2 + 4}{3}}$

Step 2.5.4

Add $2$ and $4$ .

$1 - x^{\frac{2}{3}} + x^{\frac{4}{3}} - x^{\frac{6}{3}}$

Step 2.5.5

Divide $6$ by $3$ .

$1 - x^{\frac{2}{3}} + x^{\frac{4}{3}} - x^{2}$