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

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

Step 1

Rewrite ${(5 - \sqrt{5 x})}^{2}$ as $(5 - \sqrt{5 x}) (5 - \sqrt{5 x})$ .

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $5$ by $5$ .

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

Multiply $- 1$ by $5$ .

$25 - 5 \sqrt{5 x} - \sqrt{5 x} \cdot 5 - \sqrt{5 x} (- \sqrt{5 x})$

Multiply $5$ by $- 1$ .

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

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

Multiply $- 1$ by $- 1$ .

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

Multiply $\sqrt{5 x}$ by $1$ .

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

Raise $\sqrt{5 x}$ to the power of $1$ .

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

Raise $\sqrt{5 x}$ to the power of $1$ .

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

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

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

Add $1$ and $1$ .

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

Rewrite ${\sqrt{5 x}}^{2}$ as $5 x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 x}$ as ${(5 x)}^{\frac{1}{2}}$ .

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Subtract $5 \sqrt{5 x}$ from $- 5 \sqrt{5 x}$ .

$25 - 10 \sqrt{5 x} + 5 x$

Step 4

Move $- 10 \sqrt{5 x}$ .

$25 + 5 x - 10 \sqrt{5 x}$

Step 5

Reorder $25$ and $5 x$ .

$5 x + 25 - 10 \sqrt{5 x}$

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

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