Algebra Examples

$(\sqrt{5} x + 7) (\sqrt{5} x - 7)$

Step 1

Expand $(\sqrt{5} x + 7) (\sqrt{5} x - 7)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$\sqrt{5} x (\sqrt{5} x - 7) + 7 (\sqrt{5} x - 7)$

Step 1.2

Apply the distributive property.

$\sqrt{5} x (\sqrt{5} x) + \sqrt{5} x \cdot - 7 + 7 (\sqrt{5} x - 7)$

Step 1.3

Apply the distributive property.

$\sqrt{5} x (\sqrt{5} x) + \sqrt{5} x \cdot - 7 + 7 (\sqrt{5} x) + 7 \cdot - 7$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $\sqrt{5} x (\sqrt{5} x) + \sqrt{5} x \cdot - 7 + 7 (\sqrt{5} x) + 7 \cdot - 7$ .

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Step 2.1.1

Reorder the factors in the terms $\sqrt{5} x \cdot - 7$ and $7 (\sqrt{5} x)$ .

$\sqrt{5} x (\sqrt{5} x) - 7 x \sqrt{5} + 7 x \sqrt{5} + 7 \cdot - 7$

Step 2.1.2

Add $- 7 x \sqrt{5}$ and $7 x \sqrt{5}$ .

$\sqrt{5} x (\sqrt{5} x) + 0 + 7 \cdot - 7$

Step 2.1.3

Add $\sqrt{5} x (\sqrt{5} x)$ and $0$ .

$\sqrt{5} x (\sqrt{5} x) + 7 \cdot - 7$

Step 2.2

Simplify each term.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

$\sqrt{5} \cdot \sqrt{5} x \cdot x + 7 \cdot - 7$

Step 2.2.2

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

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Step 2.2.2.1

Move $x$ .

$\sqrt{5} \cdot \sqrt{5} (x \cdot x) + 7 \cdot - 7$

Step 2.2.2.2

Multiply $x$ by $x$ .

$\sqrt{5} \cdot \sqrt{5} x^{2} + 7 \cdot - 7$

Step 2.2.3

Combine using the product rule for radicals.

$\sqrt{5 \cdot 5} x^{2} + 7 \cdot - 7$

Step 2.2.4

Multiply $5$ by $5$ .

$\sqrt{25} x^{2} + 7 \cdot - 7$

Step 2.2.5

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2}} x^{2} + 7 \cdot - 7$

Step 2.2.6

Pull terms out from under the radical, assuming positive real numbers.

$5 x^{2} + 7 \cdot - 7$

Step 2.2.7

Multiply $7$ by $- 7$ .

$5 x^{2} - 49$