Simplify (4-x square root of 7)^2

${(4 - x \sqrt{7})}^{2}$

Step 1

Rewrite ${(4 - x \sqrt{7})}^{2}$ as $(4 - x \sqrt{7}) (4 - x \sqrt{7})$ .

$(4 - x \sqrt{7}) (4 - x \sqrt{7})$

Step 2

Expand $(4 - x \sqrt{7}) (4 - x \sqrt{7})$ using the FOIL Method.

Apply the distributive property.

$4 (4 - x \sqrt{7}) - x \sqrt{7} (4 - x \sqrt{7})$

Apply the distributive property.

$4 \cdot 4 + 4 (- x \sqrt{7}) - x \sqrt{7} (4 - x \sqrt{7})$

Apply the distributive property.

$4 \cdot 4 + 4 (- x \sqrt{7}) - x \sqrt{7} \cdot 4 - x \sqrt{7} (- x \sqrt{7})$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $4$ by $4$ .

$16 + 4 (- x \sqrt{7}) - x \sqrt{7} \cdot 4 - x \sqrt{7} (- x \sqrt{7})$

Multiply $- 1$ by $4$ .

$16 - 4 (x \sqrt{7}) - x \sqrt{7} \cdot 4 - x \sqrt{7} (- x \sqrt{7})$

Multiply $4$ by $- 1$ .

$16 - 4 x \sqrt{7} - 4 x \sqrt{7} - x \sqrt{7} (- x \sqrt{7})$

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

Move $x$ .

$16 - 4 x \sqrt{7} - 4 x \sqrt{7} - (x \cdot x) \sqrt{7} (- 1 \sqrt{7})$

Multiply $x$ by $x$ .

$16 - 4 x \sqrt{7} - 4 x \sqrt{7} - x^{2} \sqrt{7} (- 1 \sqrt{7})$

Rewrite $- 1 \sqrt{7}$ as $- \sqrt{7}$ .

$16 - 4 x \sqrt{7} - 4 x \sqrt{7} - x^{2} \sqrt{7} (- \sqrt{7})$

Multiply $- x^{2} \sqrt{7} (- \sqrt{7})$ .

Multiply $- 1$ by $- 1$ .

$16 - 4 x \sqrt{7} - 4 x \sqrt{7} + 1 x^{2} \sqrt{7} \sqrt{7}$

Multiply $x^{2}$ by $1$ .

$16 - 4 x \sqrt{7} - 4 x \sqrt{7} + x^{2} \sqrt{7} \sqrt{7}$

Raise $\sqrt{7}$ to the power of $1$ .

$16 - 4 x \sqrt{7} - 4 x \sqrt{7} + x^{2} ({\sqrt{7}}^{1} \sqrt{7})$

Raise $\sqrt{7}$ to the power of $1$ .

$16 - 4 x \sqrt{7} - 4 x \sqrt{7} + x^{2} ({\sqrt{7}}^{1} {\sqrt{7}}^{1})$

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

$16 - 4 x \sqrt{7} - 4 x \sqrt{7} + x^{2} {\sqrt{7}}^{1 + 1}$

Add $1$ and $1$ .

$16 - 4 x \sqrt{7} - 4 x \sqrt{7} + x^{2} {\sqrt{7}}^{2}$

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$16 - 4 x \sqrt{7} - 4 x \sqrt{7} + x^{2} {(7^{\frac{1}{2}})}^{2}$

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

$16 - 4 x \sqrt{7} - 4 x \sqrt{7} + x^{2} \cdot 7^{\frac{1}{2} \cdot 2}$

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

$16 - 4 x \sqrt{7} - 4 x \sqrt{7} + x^{2} \cdot 7^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$16 - 4 x \sqrt{7} - 4 x \sqrt{7} + x^{2} \cdot 7^{\frac{2}{2}}$

Rewrite the expression.

$16 - 4 x \sqrt{7} - 4 x \sqrt{7} + x^{2} \cdot 7^{1}$

Evaluate the exponent.

$16 - 4 x \sqrt{7} - 4 x \sqrt{7} + x^{2} \cdot 7$

Move $7$ to the left of $x^{2}$ .

$16 - 4 x \sqrt{7} - 4 x \sqrt{7} + 7 x^{2}$

Subtract $4 x \sqrt{7}$ from $- 4 x \sqrt{7}$ .

$16 - 8 x \sqrt{7} + 7 x^{2}$

Simplify (4-x square root of 7)^2

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