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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

$4 \cdot 4 + 4 \sqrt{x} - \sqrt{x} \cdot 4 - \sqrt{x} \sqrt{x}$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $4$ by $4$ .

$16 + 4 \sqrt{x} - \sqrt{x} \cdot 4 - \sqrt{x} \sqrt{x}$

Multiply $4$ by $- 1$ .

$16 + 4 \sqrt{x} - 4 \sqrt{x} - \sqrt{x} \sqrt{x}$

Multiply $- \sqrt{x} \sqrt{x}$ .

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

$16 + 4 \sqrt{x} - 4 \sqrt{x} - ({\sqrt{x}}^{1} \sqrt{x})$

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

$16 + 4 \sqrt{x} - 4 \sqrt{x} - ({\sqrt{x}}^{1} {\sqrt{x}}^{1})$

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

$16 + 4 \sqrt{x} - 4 \sqrt{x} - {\sqrt{x}}^{1 + 1}$

Add $1$ and $1$ .

$16 + 4 \sqrt{x} - 4 \sqrt{x} - {\sqrt{x}}^{2}$

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

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

$16 + 4 \sqrt{x} - 4 \sqrt{x} - {(x^{\frac{1}{2}})}^{2}$

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

$16 + 4 \sqrt{x} - 4 \sqrt{x} - x^{\frac{1}{2} \cdot 2}$

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

$16 + 4 \sqrt{x} - 4 \sqrt{x} - x^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$16 + 4 \sqrt{x} - 4 \sqrt{x} - x^{\frac{2}{2}}$

Rewrite the expression.

$16 + 4 \sqrt{x} - 4 \sqrt{x} - x^{1}$

Simplify.

$16 + 4 \sqrt{x} - 4 \sqrt{x} - x$

Subtract $4 \sqrt{x}$ from $4 \sqrt{x}$ .

$16 + 0 - x$

Add $16$ and $0$ .

$16 - x$