Simplify (2x^(1/3)+3)(2x^(1/3)-3)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

Multiply $x^{\frac{1}{3}}$ by $x^{\frac{1}{3}}$ by adding the exponents.

Move $x^{\frac{1}{3}}$ .

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

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

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

Combine the numerators over the common denominator.

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

Add $1$ and $1$ .

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

Multiply $2$ by $2$ .

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

Multiply $- 3$ by $2$ .

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

Multiply $2$ by $3$ .

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

Multiply $3$ by $- 3$ .

$4 x^{\frac{2}{3}} - 6 x^{\frac{1}{3}} + 6 x^{\frac{1}{3}} - 9$

Add $- 6 x^{\frac{1}{3}}$ and $6 x^{\frac{1}{3}}$ .

$4 x^{\frac{2}{3}} + 0 - 9$

Add $4 x^{\frac{2}{3}}$ and $0$ .

$4 x^{\frac{2}{3}} - 9$