Pre-Algebra Examples

$\frac{2 a^{3} + a^{2}}{5 b^{2}}$

Step 1

Factor $a^{2}$ out of $2 a^{3} + a^{2}$ .

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Step 1.1

Factor $a^{2}$ out of $2 a^{3}$ .

$\frac{a^{2} (2 a) + a^{2}}{5 b^{2}}$

Step 1.2

Multiply by $1$ .

$\frac{a^{2} (2 a) + a^{2} \cdot 1}{5 b^{2}}$

Step 1.3

Factor $a^{2}$ out of $a^{2} (2 a) + a^{2} \cdot 1$ .

$\frac{a^{2} (2 a + 1)}{5 b^{2}}$

Step 2

Apply the distributive property.

$\frac{a^{2} (2 a) + a^{2} \cdot 1}{5 b^{2}}$

Step 3

Rewrite using the commutative property of multiplication.

$\frac{2 a^{2} a + a^{2} \cdot 1}{5 b^{2}}$

Step 4

Multiply $a^{2}$ by $1$ .

$\frac{2 a^{2} a + a^{2}}{5 b^{2}}$

Step 5

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

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Step 5.1

Move $a$ .

$\frac{2 (a \cdot a^{2}) + a^{2}}{5 b^{2}}$

Step 5.2

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

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Step 5.2.1

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

$\frac{2 (a^{1} a^{2}) + a^{2}}{5 b^{2}}$

Step 5.2.2

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

$\frac{2 a^{1 + 2} + a^{2}}{5 b^{2}}$

Step 5.3

Add $1$ and $2$ .

$\frac{2 a^{3} + a^{2}}{5 b^{2}}$

Step 6

Split the fraction $\frac{2 a^{3} + a^{2}}{5 b^{2}}$ into two fractions.

$\frac{2 a^{3}}{5 b^{2}} + \frac{a^{2}}{5 b^{2}}$