Simplify (5 square root of x- square root of 2)(5 square root of x+ square root of 2)

$(5 \sqrt{x} - \sqrt{2}) (5 \sqrt{x} + \sqrt{2})$

Step 1

Expand $(5 \sqrt{x} - \sqrt{2}) (5 \sqrt{x} + \sqrt{2})$ using the FOIL Method.

Apply the distributive property.

$5 \sqrt{x} (5 \sqrt{x} + \sqrt{2}) - \sqrt{2} (5 \sqrt{x} + \sqrt{2})$

Apply the distributive property.

$5 \sqrt{x} (5 \sqrt{x}) + 5 \sqrt{x} \sqrt{2} - \sqrt{2} (5 \sqrt{x} + \sqrt{2})$

Apply the distributive property.

$5 \sqrt{x} (5 \sqrt{x}) + 5 \sqrt{x} \sqrt{2} - \sqrt{2} (5 \sqrt{x}) - \sqrt{2} \sqrt{2}$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $5 \sqrt{x} (5 \sqrt{x})$ .

Multiply $5$ by $5$ .

$25 \sqrt{x} \sqrt{x} + 5 \sqrt{x} \sqrt{2} - \sqrt{2} (5 \sqrt{x}) - \sqrt{2} \sqrt{2}$

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

$25 ({\sqrt{x}}^{1} \sqrt{x}) + 5 \sqrt{x} \sqrt{2} - \sqrt{2} (5 \sqrt{x}) - \sqrt{2} \sqrt{2}$

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

$25 ({\sqrt{x}}^{1} {\sqrt{x}}^{1}) + 5 \sqrt{x} \sqrt{2} - \sqrt{2} (5 \sqrt{x}) - \sqrt{2} \sqrt{2}$

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

$25 {\sqrt{x}}^{1 + 1} + 5 \sqrt{x} \sqrt{2} - \sqrt{2} (5 \sqrt{x}) - \sqrt{2} \sqrt{2}$

Add $1$ and $1$ .

$25 {\sqrt{x}}^{2} + 5 \sqrt{x} \sqrt{2} - \sqrt{2} (5 \sqrt{x}) - \sqrt{2} \sqrt{2}$

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

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

$25 {(x^{\frac{1}{2}})}^{2} + 5 \sqrt{x} \sqrt{2} - \sqrt{2} (5 \sqrt{x}) - \sqrt{2} \sqrt{2}$

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

$25 x^{\frac{1}{2} \cdot 2} + 5 \sqrt{x} \sqrt{2} - \sqrt{2} (5 \sqrt{x}) - \sqrt{2} \sqrt{2}$

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

$25 x^{\frac{2}{2}} + 5 \sqrt{x} \sqrt{2} - \sqrt{2} (5 \sqrt{x}) - \sqrt{2} \sqrt{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$25 x^{\frac{2}{2}} + 5 \sqrt{x} \sqrt{2} - \sqrt{2} (5 \sqrt{x}) - \sqrt{2} \sqrt{2}$

Rewrite the expression.

$25 x^{1} + 5 \sqrt{x} \sqrt{2} - \sqrt{2} (5 \sqrt{x}) - \sqrt{2} \sqrt{2}$

Simplify.

$25 x + 5 \sqrt{x} \sqrt{2} - \sqrt{2} (5 \sqrt{x}) - \sqrt{2} \sqrt{2}$

Combine using the product rule for radicals.

$25 x + 5 \sqrt{2 x} - \sqrt{2} (5 \sqrt{x}) - \sqrt{2} \sqrt{2}$

Multiply $- \sqrt{2} (5 \sqrt{x})$ .

Multiply $5$ by $- 1$ .

$25 x + 5 \sqrt{2 x} - 5 \sqrt{2} \sqrt{x} - \sqrt{2} \sqrt{2}$

Combine using the product rule for radicals.

$25 x + 5 \sqrt{2 x} - 5 \sqrt{x \cdot 2} - \sqrt{2} \sqrt{2}$

Multiply $- \sqrt{2} \sqrt{2}$ .

Raise $\sqrt{2}$ to the power of $1$ .

$25 x + 5 \sqrt{2 x} - 5 \sqrt{x \cdot 2} - ({\sqrt{2}}^{1} \sqrt{2})$

Raise $\sqrt{2}$ to the power of $1$ .

$25 x + 5 \sqrt{2 x} - 5 \sqrt{x \cdot 2} - ({\sqrt{2}}^{1} {\sqrt{2}}^{1})$

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

$25 x + 5 \sqrt{2 x} - 5 \sqrt{x \cdot 2} - {\sqrt{2}}^{1 + 1}$

Add $1$ and $1$ .

$25 x + 5 \sqrt{2 x} - 5 \sqrt{x \cdot 2} - {\sqrt{2}}^{2}$

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

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

$25 x + 5 \sqrt{2 x} - 5 \sqrt{x \cdot 2} - {(2^{\frac{1}{2}})}^{2}$

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

$25 x + 5 \sqrt{2 x} - 5 \sqrt{x \cdot 2} - 2^{\frac{1}{2} \cdot 2}$

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

$25 x + 5 \sqrt{2 x} - 5 \sqrt{x \cdot 2} - 2^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$25 x + 5 \sqrt{2 x} - 5 \sqrt{x \cdot 2} - 2^{\frac{2}{2}}$

Rewrite the expression.

$25 x + 5 \sqrt{2 x} - 5 \sqrt{x \cdot 2} - 2^{1}$

Evaluate the exponent.

$25 x + 5 \sqrt{2 x} - 5 \sqrt{x \cdot 2} - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$25 x + 5 \sqrt{2 x} - 5 \sqrt{x \cdot 2} - 2$

Subtract $5 \sqrt{x \cdot 2}$ from $5 \sqrt{2 x}$ .

Reorder $x$ and $2$ .

$25 x + 5 \sqrt{2 x} - 5 \sqrt{2 \cdot x} - 2$

Subtract $5 \sqrt{2 \cdot x}$ from $5 \sqrt{2 x}$ .

$25 x + 0 - 2$

Add $25 x$ and $0$ .

$25 x - 2$

Simplify (5 square root of x- square root of 2)(5 square root of x+ square root of 2)

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