Pre-Algebra Examples

$x^{2} y^{2}$ , $10 x y^{2} \cdot (2 x^{2} y^{2})$

Step 1

Factor $x y^{2}$ out of $x^{2} y^{2} + 10 x y^{2} \cdot (2 x^{2} y^{2})$ .

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Step 1.1

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

$x y^{2} (x) + 10 x y^{2} \cdot (2 x^{2} y^{2})$

Step 1.2

Factor $x y^{2}$ out of $10 x y^{2} \cdot (2 x^{2} y^{2})$ .

$x y^{2} (x) + x y^{2} (10 \cdot (2 x^{2} y^{2}))$

Step 1.3

Factor $x y^{2}$ out of $x y^{2} (x) + x y^{2} (10 \cdot (2 x^{2} y^{2}))$ .

$x y^{2} (x + 10 \cdot (2 x^{2} y^{2}))$

Step 2

Multiply $2$ by $10$ .

$x y^{2} (x + 20 \cdot (x^{2} y^{2}))$

Step 3

Remove parentheses.

$x y^{2} (x + 20 \cdot x^{2} y^{2})$

Step 4

Factor $x$ out of $x + 20 \cdot x^{2} y^{2}$ .

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Step 4.1

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

$x y^{2} (x^{1} + 20 \cdot x^{2} y^{2})$

Step 4.2

Factor $x$ out of $x^{1}$ .

$x y^{2} (x \cdot 1 + 20 \cdot x^{2} y^{2})$

Step 4.3

Factor $x$ out of $20 \cdot x^{2} y^{2}$ .

$x y^{2} (x \cdot 1 + x (20 \cdot x y^{2}))$

Step 4.4

Factor $x$ out of $x \cdot 1 + x (20 \cdot x y^{2})$ .

$x y^{2} (x (1 + 20 \cdot x y^{2}))$

$x y^{2} (x (1 + 20 x y^{2}))$

Step 5

Remove unnecessary parentheses.

$x y^{2} x (1 + 20 x y^{2})$

Step 6

Combine exponents.

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Step 6.1

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

$x^{1} x y^{2} (1 + 20 x y^{2})$

Step 6.2

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

$x^{1} x^{1} y^{2} (1 + 20 x y^{2})$

Step 6.3

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

$x^{1 + 1} y^{2} (1 + 20 x y^{2})$

Step 6.4

Add $1$ and $1$ .

$x^{2} y^{2} (1 + 20 x y^{2})$

Step 7

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

$x^{2} y^{2}$