Basic Math Examples

$(\sqrt{15} - 7) (7 + \sqrt{15})$

Step 1

Expand $(\sqrt{15} - 7) (7 + \sqrt{15})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$\sqrt{15} (7 + \sqrt{15}) - 7 (7 + \sqrt{15})$

Step 1.2

Apply the distributive property.

$\sqrt{15} \cdot 7 + \sqrt{15} \sqrt{15} - 7 (7 + \sqrt{15})$

Step 1.3

Apply the distributive property.

$\sqrt{15} \cdot 7 + \sqrt{15} \sqrt{15} - 7 \cdot 7 - 7 \sqrt{15}$

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

Move $7$ to the left of $\sqrt{15}$ .

$7 \cdot \sqrt{15} + \sqrt{15} \sqrt{15} - 7 \cdot 7 - 7 \sqrt{15}$

Step 2.1.2

Combine using the product rule for radicals.

$7 \sqrt{15} + \sqrt{15 \cdot 15} - 7 \cdot 7 - 7 \sqrt{15}$

Step 2.1.3

Multiply $15$ by $15$ .

$7 \sqrt{15} + \sqrt{225} - 7 \cdot 7 - 7 \sqrt{15}$

Step 2.1.4

Rewrite $225$ as $15^{2}$ .

$7 \sqrt{15} + \sqrt{15^{2}} - 7 \cdot 7 - 7 \sqrt{15}$

Step 2.1.5

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

$7 \sqrt{15} + 15 - 7 \cdot 7 - 7 \sqrt{15}$

Step 2.1.6

Multiply $- 7$ by $7$ .

$7 \sqrt{15} + 15 - 49 - 7 \sqrt{15}$

Step 2.2

Subtract $7 \sqrt{15}$ from $7 \sqrt{15}$ .

$0 + 15 - 49$

Step 2.3

Add $0$ and $15$ .

$15 - 49$

Step 2.4

Subtract $49$ from $15$ .

$- 34$