Pre-Algebra Examples

$- 30 x y^{2}$ , $15 x^{3} y^{3} \cdot (60 x^{2} y^{3})$

Step 1

Factor $- 15 x y^{2}$ out of $- 30 x y^{2} + 15 x^{3} y^{3} \cdot (60 x^{2} y^{3})$ .

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Step 1.1

Reorder the expression.

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Step 1.1.1

Move parentheses.

$- 30 x y^{2} + 15 x^{3} y^{3} \cdot (60 x^{2}) y^{3}$

Step 1.1.2

Remove parentheses.

$- 30 x y^{2} + 15 x^{3} y^{3} \cdot 60 x^{2} y^{3}$

Step 1.1.3

Move $y^{3}$ .

$- 30 x y^{2} + 15 x^{3} \cdot 60 x^{2} y^{3} y^{3}$

Step 1.1.4

Move $x^{3}$ .

$- 30 x y^{2} + 15 \cdot 60 x^{3} x^{2} y^{3} y^{3}$

Step 1.1.5

Reorder $- 30 x y^{2}$ and $15 \cdot 60 x^{3} x^{2} y^{3} y^{3}$ .

$15 \cdot 60 x^{3} x^{2} y^{3} y^{3} - 30 x y^{2}$

Step 1.2

Factor $- 15 x y^{2}$ out of $15 \cdot 60 x^{3} x^{2} y^{3} y^{3}$ .

$- 15 x y^{2} (- 1 \cdot 60 x^{2} x^{2} y \cdot y^{3}) - 30 x y^{2}$

Step 1.3

Factor $- 15 x y^{2}$ out of $- 30 x y^{2}$ .

$- 15 x y^{2} (- 1 \cdot 60 x^{2} x^{2} y \cdot y^{3}) - 15 x y^{2} (2)$

Step 1.4

Factor $- 15 x y^{2}$ out of $- 15 x y^{2} (- 1 \cdot 60 x^{2} x^{2} y \cdot y^{3}) - 15 x y^{2} (2)$ .

$- 15 x y^{2} (- 1 \cdot 60 x^{2} x^{2} y \cdot y^{3} + 2)$

Step 2

Combine exponents.

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Step 2.1

Multiply $- 1$ by $60$ .

$- 15 x y^{2} (- 60 x^{2} x^{2} y \cdot y^{3} + 2)$

Step 2.2

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

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Step 2.2.1

Move $x^{2}$ .

$- 15 x y^{2} (- 60 (x^{2} x^{2}) y \cdot y^{3} + 2)$

Step 2.2.2

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

$- 15 x y^{2} (- 60 x^{2 + 2} y \cdot y^{3} + 2)$

Step 2.2.3

Add $2$ and $2$ .

$- 15 x y^{2} (- 60 x^{4} y \cdot y^{3} + 2)$

Step 2.3

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

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Step 2.3.1

Move $y^{3}$ .

$- 15 x y^{2} (- 60 x^{4} (y^{3} y) + 2)$

Step 2.3.2

Multiply $y^{3}$ by $y$ .

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Step 2.3.2.1

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

$- 15 x y^{2} (- 60 x^{4} (y^{3} y^{1}) + 2)$

Step 2.3.2.2

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

$- 15 x y^{2} (- 60 x^{4} y^{3 + 1} + 2)$

Step 2.3.3

Add $3$ and $1$ .

$- 15 x y^{2} (- 60 x^{4} y^{4} + 2)$

Step 3

Factor.

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Step 3.1

Factor $- 2$ out of $- 60 x^{4} y^{4} + 2$ .

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Step 3.1.1

Factor $- 2$ out of $- 60 x^{4} y^{4}$ .

$- 15 x y^{2} (- 2 (30 x^{4} y^{4}) + 2)$

Step 3.1.2

Factor $- 2$ out of $2$ .

$- 15 x y^{2} (- 2 (30 x^{4} y^{4}) - 2 (- 1))$

Step 3.1.3

Factor $- 2$ out of $- 2 (30 x^{4} y^{4}) - 2 (- 1)$ .

$- 15 x y^{2} (- 2 (30 x^{4} y^{4} - 1))$

Step 3.2

Remove unnecessary parentheses.

$- 15 x y^{2} \cdot - 2 (30 x^{4} y^{4} - 1)$

Step 4

Multiply $- 2$ by $- 15$ .

$30 x y^{2} (30 x^{4} y^{4} - 1)$

Step 5

The greatest common factor $GCF$ is the term in front of the factored expression.

$30 x y^{2}$