Trigonometry Examples

$\frac{12 x^{14} y^{9} - 15 x^{8} y^{12}}{3 x^{2} y^{3}}$

Step 1

Simplify terms.

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Step 1.1

Factor $3 x^{8} y^{9}$ out of $12 x^{14} y^{9} - 15 x^{8} y^{12}$ .

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Step 1.1.1

Factor $3 x^{8} y^{9}$ out of $12 x^{14} y^{9}$ .

$\frac{3 x^{8} y^{9} (4 x^{6}) - 15 x^{8} y^{12}}{3 x^{2} y^{3}}$

Step 1.1.2

Factor $3 x^{8} y^{9}$ out of $- 15 x^{8} y^{12}$ .

$\frac{3 x^{8} y^{9} (4 x^{6}) + 3 x^{8} y^{9} (- 5 y^{3})}{3 x^{2} y^{3}}$

Step 1.1.3

Factor $3 x^{8} y^{9}$ out of $3 x^{8} y^{9} (4 x^{6}) + 3 x^{8} y^{9} (- 5 y^{3})$ .

$\frac{3 x^{8} y^{9} (4 x^{6} - 5 y^{3})}{3 x^{2} y^{3}}$

Step 1.2

Cancel the common factor of $3$ .

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Step 1.2.1

Cancel the common factor.

$\frac{3 x^{8} y^{9} (4 x^{6} - 5 y^{3})}{3 x^{2} y^{3}}$

Step 1.2.2

Rewrite the expression.

$\frac{x^{8} y^{9} (4 x^{6} - 5 y^{3})}{x^{2} y^{3}}$

Step 1.3

Cancel the common factor of $x^{8}$ and $x^{2}$ .

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Step 1.3.1

Factor $x^{2}$ out of $x^{8} y^{9} (4 x^{6} - 5 y^{3})$ .

$\frac{x^{2} (x^{6} y^{9} (4 x^{6} - 5 y^{3}))}{x^{2} y^{3}}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $x^{2}$ out of $x^{2} y^{3}$ .

$\frac{x^{2} (x^{6} y^{9} (4 x^{6} - 5 y^{3}))}{x^{2} (y^{3})}$

Step 1.3.2.2

Cancel the common factor.

$\frac{x^{2} (x^{6} y^{9} (4 x^{6} - 5 y^{3}))}{x^{2} y^{3}}$

Step 1.3.2.3

Rewrite the expression.

$\frac{x^{6} y^{9} (4 x^{6} - 5 y^{3})}{y^{3}}$

Step 1.4

Cancel the common factor of $y^{9}$ and $y^{3}$ .

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Step 1.4.1

Factor $y^{3}$ out of $x^{6} y^{9} (4 x^{6} - 5 y^{3})$ .

$\frac{y^{3} (x^{6} y^{6} (4 x^{6} - 5 y^{3}))}{y^{3}}$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Multiply by $1$ .

$\frac{y^{3} (x^{6} y^{6} (4 x^{6} - 5 y^{3}))}{y^{3} \cdot 1}$

Step 1.4.2.2

Cancel the common factor.

$\frac{y^{3} (x^{6} y^{6} (4 x^{6} - 5 y^{3}))}{y^{3} \cdot 1}$

Step 1.4.2.3

Rewrite the expression.

$\frac{x^{6} y^{6} (4 x^{6} - 5 y^{3})}{1}$

Step 1.4.2.4

Divide $x^{6} y^{6} (4 x^{6} - 5 y^{3})$ by $1$ .

$x^{6} y^{6} (4 x^{6} - 5 y^{3})$

Step 1.5

Apply the distributive property.

$x^{6} y^{6} (4 x^{6}) + x^{6} y^{6} (- 5 y^{3})$

Step 1.6

Reorder.

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Step 1.6.1

Rewrite using the commutative property of multiplication.

$4 x^{6} y^{6} x^{6} + x^{6} y^{6} (- 5 y^{3})$

Step 1.6.2

Rewrite using the commutative property of multiplication.

$4 x^{6} y^{6} x^{6} - 5 x^{6} y^{6} y^{3}$

Step 2

Simplify each term.

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Step 2.1

Multiply $x^{6}$ by $x^{6}$ by adding the exponents.

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Step 2.1.1

Move $x^{6}$ .

$4 (x^{6} x^{6}) y^{6} - 5 x^{6} y^{6} y^{3}$

Step 2.1.2

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

$4 x^{6 + 6} y^{6} - 5 x^{6} y^{6} y^{3}$

Step 2.1.3

Add $6$ and $6$ .

$4 x^{12} y^{6} - 5 x^{6} y^{6} y^{3}$

Step 2.2

Multiply $y^{6}$ by $y^{3}$ by adding the exponents.

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Step 2.2.1

Move $y^{3}$ .

$4 x^{12} y^{6} - 5 x^{6} (y^{3} y^{6})$

Step 2.2.2

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

$4 x^{12} y^{6} - 5 x^{6} y^{3 + 6}$

Step 2.2.3

Add $3$ and $6$ .

$4 x^{12} y^{6} - 5 x^{6} y^{9}$