Algebra Examples

$(7 \sqrt{2} + x) (7 \sqrt{2} - x)$

Step 1

Expand $(7 \sqrt{2} + x) (7 \sqrt{2} - x)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$7 \sqrt{2} (7 \sqrt{2} - x) + x (7 \sqrt{2} - x)$

Step 1.2

Apply the distributive property.

$7 \sqrt{2} (7 \sqrt{2}) + 7 \sqrt{2} (- x) + x (7 \sqrt{2} - x)$

Step 1.3

Apply the distributive property.

$7 \sqrt{2} (7 \sqrt{2}) + 7 \sqrt{2} (- x) + x (7 \sqrt{2}) + x (- x)$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $7 \sqrt{2} (7 \sqrt{2})$ .

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Step 2.1.1.1

Multiply $7$ by $7$ .

$49 \sqrt{2} \sqrt{2} + 7 \sqrt{2} (- x) + x (7 \sqrt{2}) + x (- x)$

Step 2.1.1.2

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

$49 ({\sqrt{2}}^{1} \sqrt{2}) + 7 \sqrt{2} (- x) + x (7 \sqrt{2}) + x (- x)$

Step 2.1.1.3

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

$49 ({\sqrt{2}}^{1} {\sqrt{2}}^{1}) + 7 \sqrt{2} (- x) + x (7 \sqrt{2}) + x (- x)$

Step 2.1.1.4

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

$49 {\sqrt{2}}^{1 + 1} + 7 \sqrt{2} (- x) + x (7 \sqrt{2}) + x (- x)$

Step 2.1.1.5

Add $1$ and $1$ .

$49 {\sqrt{2}}^{2} + 7 \sqrt{2} (- x) + x (7 \sqrt{2}) + x (- x)$

Step 2.1.2

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

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Step 2.1.2.1

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

$49 {(2^{\frac{1}{2}})}^{2} + 7 \sqrt{2} (- x) + x (7 \sqrt{2}) + x (- x)$

Step 2.1.2.2

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

$49 \cdot 2^{\frac{1}{2} \cdot 2} + 7 \sqrt{2} (- x) + x (7 \sqrt{2}) + x (- x)$

Step 2.1.2.3

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

$49 \cdot 2^{\frac{2}{2}} + 7 \sqrt{2} (- x) + x (7 \sqrt{2}) + x (- x)$

Step 2.1.2.4

Cancel the common factor of $2$ .

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Step 2.1.2.4.1

Cancel the common factor.

$49 \cdot 2^{\frac{2}{2}} + 7 \sqrt{2} (- x) + x (7 \sqrt{2}) + x (- x)$

Step 2.1.2.4.2

Rewrite the expression.

$49 \cdot 2^{1} + 7 \sqrt{2} (- x) + x (7 \sqrt{2}) + x (- x)$

Step 2.1.2.5

Evaluate the exponent.

$49 \cdot 2 + 7 \sqrt{2} (- x) + x (7 \sqrt{2}) + x (- x)$

Step 2.1.3

Multiply $49$ by $2$ .

$98 + 7 \sqrt{2} (- x) + x (7 \sqrt{2}) + x (- x)$

Step 2.1.4

Multiply $- 1$ by $7$ .

$98 - 7 \sqrt{2} x + x (7 \sqrt{2}) + x (- x)$

Step 2.1.5

Move $7$ to the left of $x$ .

$98 - 7 \sqrt{2} x + 7 \cdot x \sqrt{2} + x (- x)$

Step 2.1.6

Rewrite using the commutative property of multiplication.

$98 - 7 \sqrt{2} x + 7 x \sqrt{2} - x \cdot x$

Step 2.1.7

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

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Step 2.1.7.1

Move $x$ .

$98 - 7 \sqrt{2} x + 7 x \sqrt{2} - (x \cdot x)$

Step 2.1.7.2

Multiply $x$ by $x$ .

$98 - 7 \sqrt{2} x + 7 x \sqrt{2} - x^{2}$

Step 2.2

Reorder the factors of $- 7 \sqrt{2} x$ .

$98 - 7 x \sqrt{2} + 7 x \sqrt{2} - x^{2}$

Step 2.3

Add $- 7 x \sqrt{2}$ and $7 x \sqrt{2}$ .

$98 + 0 - x^{2}$

Step 2.4

Add $98$ and $0$ .

$98 - x^{2}$