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

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $2$ .

$4 + 2 (x \sqrt{5}) + x \sqrt{5} \cdot 2 + x \sqrt{5} (x \sqrt{5})$

Move $2$ to the left of $x \sqrt{5}$ .

$4 + 2 x \sqrt{5} + 2 \cdot (x \sqrt{5}) + x \sqrt{5} (x \sqrt{5})$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$4 + 2 x \sqrt{5} + 2 x \sqrt{5} + x \cdot x \sqrt{5} \sqrt{5}$

Multiply $x$ by $x$ .

$4 + 2 x \sqrt{5} + 2 x \sqrt{5} + x^{2} \sqrt{5} \sqrt{5}$

Multiply $x^{2} \sqrt{5} \sqrt{5}$ .

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

$4 + 2 x \sqrt{5} + 2 x \sqrt{5} + x^{2} ({\sqrt{5}}^{1} \sqrt{5})$

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

$4 + 2 x \sqrt{5} + 2 x \sqrt{5} + x^{2} ({\sqrt{5}}^{1} {\sqrt{5}}^{1})$

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

$4 + 2 x \sqrt{5} + 2 x \sqrt{5} + x^{2} {\sqrt{5}}^{1 + 1}$

Add $1$ and $1$ .

$4 + 2 x \sqrt{5} + 2 x \sqrt{5} + x^{2} {\sqrt{5}}^{2}$

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

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

$4 + 2 x \sqrt{5} + 2 x \sqrt{5} + x^{2} {(5^{\frac{1}{2}})}^{2}$

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

$4 + 2 x \sqrt{5} + 2 x \sqrt{5} + x^{2} \cdot 5^{\frac{1}{2} \cdot 2}$

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

$4 + 2 x \sqrt{5} + 2 x \sqrt{5} + x^{2} \cdot 5^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 + 2 x \sqrt{5} + 2 x \sqrt{5} + x^{2} \cdot 5^{\frac{2}{2}}$

Rewrite the expression.

$4 + 2 x \sqrt{5} + 2 x \sqrt{5} + x^{2} \cdot 5^{1}$

Evaluate the exponent.

$4 + 2 x \sqrt{5} + 2 x \sqrt{5} + x^{2} \cdot 5$

Move $5$ to the left of $x^{2}$ .

$4 + 2 x \sqrt{5} + 2 x \sqrt{5} + 5 x^{2}$

Add $2 x \sqrt{5}$ and $2 x \sqrt{5}$ .

$4 + 4 x \sqrt{5} + 5 x^{2}$

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

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