Simplify (4+3 square root of x)(4-3 square root of x)

$(4 + 3 \sqrt{x}) (4 - 3 \sqrt{x})$

Step 1

Expand $(4 + 3 \sqrt{x}) (4 - 3 \sqrt{x})$ using the FOIL Method.

Apply the distributive property.

$4 (4 - 3 \sqrt{x}) + 3 \sqrt{x} (4 - 3 \sqrt{x})$

Apply the distributive property.

$4 \cdot 4 + 4 (- 3 \sqrt{x}) + 3 \sqrt{x} (4 - 3 \sqrt{x})$

Apply the distributive property.

$4 \cdot 4 + 4 (- 3 \sqrt{x}) + 3 \sqrt{x} \cdot 4 + 3 \sqrt{x} (- 3 \sqrt{x})$

Step 2

Simplify terms.

Combine the opposite terms in $4 \cdot 4 + 4 (- 3 \sqrt{x}) + 3 \sqrt{x} \cdot 4 + 3 \sqrt{x} (- 3 \sqrt{x})$ .

Reorder the factors in the terms $4 (- 3 \sqrt{x})$ and $3 \sqrt{x} \cdot 4$ .

$4 \cdot 4 - 3 \cdot 4 \sqrt{x} + 3 \cdot 4 \sqrt{x} + 3 \sqrt{x} (- 3 \sqrt{x})$

Add $- 3 \cdot 4 \sqrt{x}$ and $3 \cdot 4 \sqrt{x}$ .

$4 \cdot 4 + 0 + 3 \sqrt{x} (- 3 \sqrt{x})$

Add $4 \cdot 4$ and $0$ .

$4 \cdot 4 + 3 \sqrt{x} (- 3 \sqrt{x})$

Simplify each term.

Multiply $4$ by $4$ .

$16 + 3 \sqrt{x} (- 3 \sqrt{x})$

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

Multiply $- 3$ by $3$ .

$16 - 9 \sqrt{x} \sqrt{x}$

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

$16 - 9 ({\sqrt{x}}^{1} \sqrt{x})$

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

$16 - 9 ({\sqrt{x}}^{1} {\sqrt{x}}^{1})$

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

$16 - 9 {\sqrt{x}}^{1 + 1}$

Add $1$ and $1$ .

$16 - 9 {\sqrt{x}}^{2}$

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

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

$16 - 9 {(x^{\frac{1}{2}})}^{2}$

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

$16 - 9 x^{\frac{1}{2} \cdot 2}$

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

$16 - 9 x^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$16 - 9 x^{\frac{2}{2}}$

Rewrite the expression.

$16 - 9 x^{1}$

Simplify.

$16 - 9 x$

Simplify (4+3 square root of x)(4-3 square root of x)

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