Pre-Algebra Examples

$7 x y^{2} \cdot (49 x^{2})$ , $35 x y^{2}$

Step 1

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

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Step 1.1

Move $x^{2}$ .

$7 (x^{2} x) y^{2} \cdot 49 + 35 x y^{2}$

Step 1.2

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

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Step 1.2.1

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

$7 (x^{2} x^{1}) y^{2} \cdot 49 + 35 x y^{2}$

Step 1.2.2

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

$7 x^{2 + 1} y^{2} \cdot 49 + 35 x y^{2}$

Step 1.3

Add $2$ and $1$ .

$7 x^{3} y^{2} \cdot 49 + 35 x y^{2}$

Step 2

Multiply $49$ by $7$ .

$343 x^{3} y^{2} + 35 x y^{2}$

Step 3

Factor $7 x y^{2}$ out of $343 x^{3} y^{2} + 35 x y^{2}$ .

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Step 3.1

Factor $7 x y^{2}$ out of $343 x^{3} y^{2}$ .

$7 x y^{2} (49 x^{2}) + 35 x y^{2}$

Step 3.2

Factor $7 x y^{2}$ out of $35 x y^{2}$ .

$7 x y^{2} (49 x^{2}) + 7 x y^{2} (5)$

Step 3.3

Factor $7 x y^{2}$ out of $7 x y^{2} (49 x^{2}) + 7 x y^{2} (5)$ .

$7 x y^{2} (49 x^{2} + 5)$

Step 4

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

$7 x y^{2}$