Simplify (3 square root of x+ square root of 3)(3 square root of x- square root of 3)

$(3 \sqrt{x} + \sqrt{3}) (3 \sqrt{x} - \sqrt{3})$

Step 1

Expand $(3 \sqrt{x} + \sqrt{3}) (3 \sqrt{x} - \sqrt{3})$ using the FOIL Method.

Apply the distributive property.

$3 \sqrt{x} (3 \sqrt{x} - \sqrt{3}) + \sqrt{3} (3 \sqrt{x} - \sqrt{3})$

Apply the distributive property.

$3 \sqrt{x} (3 \sqrt{x}) + 3 \sqrt{x} (- \sqrt{3}) + \sqrt{3} (3 \sqrt{x} - \sqrt{3})$

Apply the distributive property.

$3 \sqrt{x} (3 \sqrt{x}) + 3 \sqrt{x} (- \sqrt{3}) + \sqrt{3} (3 \sqrt{x}) + \sqrt{3} (- \sqrt{3})$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $3 \sqrt{x} (3 \sqrt{x})$ .

Multiply $3$ by $3$ .

$9 \sqrt{x} \sqrt{x} + 3 \sqrt{x} (- \sqrt{3}) + \sqrt{3} (3 \sqrt{x}) + \sqrt{3} (- \sqrt{3})$

Raise $\sqrt{x}$ to the power of $1$ .

$9 ({\sqrt{x}}^{1} \sqrt{x}) + 3 \sqrt{x} (- \sqrt{3}) + \sqrt{3} (3 \sqrt{x}) + \sqrt{3} (- \sqrt{3})$

Raise $\sqrt{x}$ to the power of $1$ .

$9 ({\sqrt{x}}^{1} {\sqrt{x}}^{1}) + 3 \sqrt{x} (- \sqrt{3}) + \sqrt{3} (3 \sqrt{x}) + \sqrt{3} (- \sqrt{3})$

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

$9 {\sqrt{x}}^{1 + 1} + 3 \sqrt{x} (- \sqrt{3}) + \sqrt{3} (3 \sqrt{x}) + \sqrt{3} (- \sqrt{3})$

Add $1$ and $1$ .

$9 {\sqrt{x}}^{2} + 3 \sqrt{x} (- \sqrt{3}) + \sqrt{3} (3 \sqrt{x}) + \sqrt{3} (- \sqrt{3})$

Rewrite ${\sqrt{x}}^{2}$ as $x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

$9 {(x^{\frac{1}{2}})}^{2} + 3 \sqrt{x} (- \sqrt{3}) + \sqrt{3} (3 \sqrt{x}) + \sqrt{3} (- \sqrt{3})$

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

$9 x^{\frac{1}{2} \cdot 2} + 3 \sqrt{x} (- \sqrt{3}) + \sqrt{3} (3 \sqrt{x}) + \sqrt{3} (- \sqrt{3})$

Combine $\frac{1}{2}$ and $2$ .

$9 x^{\frac{2}{2}} + 3 \sqrt{x} (- \sqrt{3}) + \sqrt{3} (3 \sqrt{x}) + \sqrt{3} (- \sqrt{3})$

Cancel the common factor of $2$ .

Cancel the common factor.

$9 x^{\frac{2}{2}} + 3 \sqrt{x} (- \sqrt{3}) + \sqrt{3} (3 \sqrt{x}) + \sqrt{3} (- \sqrt{3})$

Rewrite the expression.

$9 x^{1} + 3 \sqrt{x} (- \sqrt{3}) + \sqrt{3} (3 \sqrt{x}) + \sqrt{3} (- \sqrt{3})$

Simplify.

$9 x + 3 \sqrt{x} (- \sqrt{3}) + \sqrt{3} (3 \sqrt{x}) + \sqrt{3} (- \sqrt{3})$

Multiply $3 \sqrt{x} (- \sqrt{3})$ .

Multiply $- 1$ by $3$ .

$9 x - 3 \sqrt{x} \sqrt{3} + \sqrt{3} (3 \sqrt{x}) + \sqrt{3} (- \sqrt{3})$

Combine using the product rule for radicals.

$9 x - 3 \sqrt{3 x} + \sqrt{3} (3 \sqrt{x}) + \sqrt{3} (- \sqrt{3})$

Combine using the product rule for radicals.

$9 x - 3 \sqrt{3 x} + 3 \sqrt{3 x} + \sqrt{3} (- \sqrt{3})$

Multiply $\sqrt{3} (- \sqrt{3})$ .

Raise $\sqrt{3}$ to the power of $1$ .

$9 x - 3 \sqrt{3 x} + 3 \sqrt{3 x} - ({\sqrt{3}}^{1} \sqrt{3})$

Raise $\sqrt{3}$ to the power of $1$ .

$9 x - 3 \sqrt{3 x} + 3 \sqrt{3 x} - ({\sqrt{3}}^{1} {\sqrt{3}}^{1})$

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

$9 x - 3 \sqrt{3 x} + 3 \sqrt{3 x} - {\sqrt{3}}^{1 + 1}$

Add $1$ and $1$ .

$9 x - 3 \sqrt{3 x} + 3 \sqrt{3 x} - {\sqrt{3}}^{2}$

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$9 x - 3 \sqrt{3 x} + 3 \sqrt{3 x} - {(3^{\frac{1}{2}})}^{2}$

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

$9 x - 3 \sqrt{3 x} + 3 \sqrt{3 x} - 3^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$9 x - 3 \sqrt{3 x} + 3 \sqrt{3 x} - 3^{1}$

Evaluate the exponent.

$9 x - 3 \sqrt{3 x} + 3 \sqrt{3 x} - 1 \cdot 3$

Multiply $- 1$ by $3$ .

$9 x - 3 \sqrt{3 x} + 3 \sqrt{3 x} - 3$

Add $- 3 \sqrt{3 x}$ and $3 \sqrt{3 x}$ .

$9 x + 0 - 3$

Add $9 x$ and $0$ .

$9 x - 3$

Simplify (3 square root of x+ square root of 3)(3 square root of x- square root of 3)

Related Questions

Support LCMGCF.com by disabling your adblocker.