Algebra Examples

$\frac{14 x^{6} y^{3} - 49 x^{5} y^{9}}{- 7 x^{4} y}$

Step 1

Simplify terms.

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Step 1.1

Factor $7 x^{5} y^{3}$ out of $14 x^{6} y^{3} - 49 x^{5} y^{9}$ .

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Step 1.1.1

Factor $7 x^{5} y^{3}$ out of $14 x^{6} y^{3}$ .

$\frac{7 x^{5} y^{3} (2 x) - 49 x^{5} y^{9}}{- 7 x^{4} y}$

Step 1.1.2

Factor $7 x^{5} y^{3}$ out of $- 49 x^{5} y^{9}$ .

$\frac{7 x^{5} y^{3} (2 x) + 7 x^{5} y^{3} (- 7 y^{6})}{- 7 x^{4} y}$

Step 1.1.3

Factor $7 x^{5} y^{3}$ out of $7 x^{5} y^{3} (2 x) + 7 x^{5} y^{3} (- 7 y^{6})$ .

$\frac{7 x^{5} y^{3} (2 x - 7 y^{6})}{- 7 x^{4} y}$

Step 1.2

Cancel the common factor of $7$ and $- 7$ .

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Step 1.2.1

Factor $7$ out of $7 x^{5} y^{3} (2 x - 7 y^{6})$ .

$\frac{7 (x^{5} y^{3} (2 x - 7 y^{6}))}{- 7 x^{4} y}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $7$ out of $- 7 x^{4} y$ .

$\frac{7 (x^{5} y^{3} (2 x - 7 y^{6}))}{7 (- x^{4} y)}$

Step 1.2.2.2

Cancel the common factor.

$\frac{7 (x^{5} y^{3} (2 x - 7 y^{6}))}{7 (- x^{4} y)}$

Step 1.2.2.3

Rewrite the expression.

$\frac{x^{5} y^{3} (2 x - 7 y^{6})}{- x^{4} y}$

Step 1.3

Cancel the common factor of $x^{5}$ and $x^{4}$ .

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Step 1.3.1

Factor $x^{4}$ out of $x^{5} y^{3} (2 x - 7 y^{6})$ .

$\frac{x^{4} (x y^{3} (2 x - 7 y^{6}))}{- x^{4} y}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $x^{4}$ out of $- x^{4} y$ .

$\frac{x^{4} (x y^{3} (2 x - 7 y^{6}))}{x^{4} (- 1 y)}$

Step 1.3.2.2

Cancel the common factor.

$\frac{x^{4} (x y^{3} (2 x - 7 y^{6}))}{x^{4} (- 1 y)}$

Step 1.3.2.3

Rewrite the expression.

$\frac{x y^{3} (2 x - 7 y^{6})}{- 1 y}$

Step 1.4

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

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Step 1.4.1

Factor $y$ out of $x y^{3} (2 x - 7 y^{6})$ .

$\frac{y (x y^{2} (2 x - 7 y^{6}))}{- 1 y}$

Step 1.4.2

Move the negative one from the denominator of $\frac{x y^{2} (2 x - 7 y^{6})}{- 1}$ .

$- 1 \cdot (x y^{2} (2 x - 7 y^{6}))$

Step 1.5

Rewrite $- 1 \cdot (x y^{2} (2 x - 7 y^{6}))$ as $- (x y^{2} (2 x - 7 y^{6}))$ .

$- (x y^{2} (2 x - 7 y^{6}))$

Step 1.6

Apply the distributive property.

$- (x y^{2} (2 x) + x y^{2} (- 7 y^{6}))$

Step 1.7

Reorder.

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Step 1.7.1

Rewrite using the commutative property of multiplication.

$- (2 x y^{2} x + x y^{2} (- 7 y^{6}))$

Step 1.7.2

Rewrite using the commutative property of multiplication.

$- (2 x y^{2} x - 7 x y^{2} y^{6})$

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

Move $x$ .

$- (2 (x \cdot x) y^{2} - 7 x y^{2} y^{6})$

Step 2.1.2

Multiply $x$ by $x$ .

$- (2 x^{2} y^{2} - 7 x y^{2} y^{6})$

Step 2.2

Multiply $y^{2}$ by $y^{6}$ by adding the exponents.

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Step 2.2.1

Move $y^{6}$ .

$- (2 x^{2} y^{2} - 7 x (y^{6} y^{2}))$

Step 2.2.2

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

$- (2 x^{2} y^{2} - 7 x y^{6 + 2})$

Step 2.2.3

Add $6$ and $2$ .

$- (2 x^{2} y^{2} - 7 x y^{8})$

Step 3

Simplify by multiplying through.

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Step 3.1

Apply the distributive property.

$- (2 x^{2} y^{2}) - (- 7 x y^{8})$

Step 3.2

Multiply.

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Step 3.2.1

Multiply $2$ by $- 1$ .

$- 2 (x^{2} y^{2}) - (- 7 x y^{8})$

Step 3.2.2

Multiply $- 7$ by $- 1$ .

$- 2 (x^{2} y^{2}) + 7 (x y^{8})$

Step 4

Remove parentheses.

$- 2 x^{2} y^{2} + 7 x y^{8}$