Trigonometry Examples

$\frac{450 p + 900}{1350 + 900 \sqrt{2}}$

Step 1

Cancel the common factor of $450 p + 900$ and $1350 + 900 \sqrt{2}$ .

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Step 1.1

Factor $450$ out of $450 p$ .

$\frac{450 (p) + 900}{1350 + 900 \sqrt{2}}$

Step 1.2

Factor $450$ out of $900$ .

$\frac{450 (p) + 450 (2)}{1350 + 900 \sqrt{2}}$

Step 1.3

Factor $450$ out of $450 (p) + 450 (2)$ .

$\frac{450 (p + 2)}{1350 + 900 \sqrt{2}}$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $450$ out of $1350$ .

$\frac{450 (p + 2)}{450 (3) + 900 \sqrt{2}}$

Step 1.4.2

Factor $450$ out of $900 \sqrt{2}$ .

$\frac{450 (p + 2)}{450 (3) + 450 (2 \sqrt{2})}$

Step 1.4.3

Factor $450$ out of $450 (3) + 450 (2 \sqrt{2})$ .

$\frac{450 (p + 2)}{450 (3 + 2 \sqrt{2})}$

Step 1.4.4

Cancel the common factor.

$\frac{450 (p + 2)}{450 (3 + 2 \sqrt{2})}$

Step 1.4.5

Rewrite the expression.

$\frac{p + 2}{3 + 2 \sqrt{2}}$

Step 2

Multiply $\frac{p + 2}{3 + 2 \sqrt{2}}$ by $\frac{3 - 2 \sqrt{2}}{3 - 2 \sqrt{2}}$ .

$\frac{p + 2}{3 + 2 \sqrt{2}} \cdot \frac{3 - 2 \sqrt{2}}{3 - 2 \sqrt{2}}$

Step 3

Combine fractions.

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Step 3.1

Multiply $\frac{p + 2}{3 + 2 \sqrt{2}}$ by $\frac{3 - 2 \sqrt{2}}{3 - 2 \sqrt{2}}$ .

$\frac{(p + 2) (3 - 2 \sqrt{2})}{(3 + 2 \sqrt{2}) (3 - 2 \sqrt{2})}$

Step 3.2

Expand the denominator using the FOIL method.

$\frac{(p + 2) (3 - 2 \sqrt{2})}{9 - 6 \sqrt{2} + 6 \sqrt{2} - 4 {\sqrt{2}}^{2}}$

Step 3.3

Simplify.

$\frac{(p + 2) (3 - 2 \sqrt{2})}{1}$

Step 3.4

Divide $(p + 2) (3 - 2 \sqrt{2})$ by $1$ .

$(p + 2) (3 - 2 \sqrt{2})$

Step 4

Expand $(p + 2) (3 - 2 \sqrt{2})$ using the FOIL Method.

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Step 4.1

Apply the distributive property.

$p (3 - 2 \sqrt{2}) + 2 (3 - 2 \sqrt{2})$

Step 4.2

Apply the distributive property.

$p \cdot 3 + p (- 2 \sqrt{2}) + 2 (3 - 2 \sqrt{2})$

Step 4.3

Apply the distributive property.

$p \cdot 3 + p (- 2 \sqrt{2}) + 2 \cdot 3 + 2 (- 2 \sqrt{2})$

Step 5

Simplify terms.

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Step 5.1

Simplify each term.

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Step 5.1.1

Move $3$ to the left of $p$ .

$3 \cdot p + p (- 2 \sqrt{2}) + 2 \cdot 3 + 2 (- 2 \sqrt{2})$

Step 5.1.2

Multiply $2$ by $3$ .

$3 p + p (- 2 \sqrt{2}) + 6 + 2 (- 2 \sqrt{2})$

Step 5.1.3

Multiply $- 2$ by $2$ .

$3 p + p (- 2 \sqrt{2}) + 6 - 4 \sqrt{2}$

Step 5.2

Reorder factors in $3 p + p (- 2 \sqrt{2}) + 6 - 4 \sqrt{2}$ .

$3 p - 2 p \sqrt{2} + 6 - 4 \sqrt{2}$