Algebra Examples

$\frac{15 x^{5} y^{4} - 25 x^{4} y^{3}}{5 x^{2} y^{3}}$

Step 1

Factor $5 x^{4} y^{3}$ out of $15 x^{5} y^{4} - 25 x^{4} y^{3}$ .

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Step 1.1

Factor $5 x^{4} y^{3}$ out of $15 x^{5} y^{4}$ .

$\frac{5 x^{4} y^{3} (3 x y) - 25 x^{4} y^{3}}{5 x^{2} y^{3}}$

Step 1.2

Factor $5 x^{4} y^{3}$ out of $- 25 x^{4} y^{3}$ .

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

Step 1.3

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

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

Step 2

Cancel the common factor of $5$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

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

Step 3

Cancel the common factor of $x^{4}$ and $x^{2}$ .

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

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

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Step 4.1

Cancel the common factor.

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

Step 4.2

Divide $x^{2} (3 x y - 5)$ by $1$ .

$x^{2} (3 x y - 5)$

Step 5

Apply the distributive property.

$x^{2} (3 x y) + x^{2} \cdot - 5$

Step 6

Rewrite using the commutative property of multiplication.

$3 x^{2} (x y) + x^{2} \cdot - 5$

Step 7

Move $- 5$ to the left of $x^{2}$ .

$3 x^{2} (x y) - 5 \cdot x^{2}$

Step 8

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 8.1

Move $x$ .

$3 (x \cdot x^{2}) y - 5 \cdot x^{2}$

Step 8.2

Multiply $x$ by $x^{2}$ .

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Step 8.2.1

Raise $x$ to the power of $1$ .

$3 (x^{1} x^{2}) y - 5 \cdot x^{2}$

Step 8.2.2

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

$3 x^{1 + 2} y - 5 \cdot x^{2}$

Step 8.3

Add $1$ and $2$ .

$3 x^{3} y - 5 \cdot x^{2}$

$3 x^{3} y - 5 x^{2}$