Pre-Algebra Examples

$(60 a^{3} - 75 a^{2}) \div 15 a$

Step 1

Rewrite the division as a fraction.

$\frac{60 a^{3} - 75 a^{2}}{15 a}$

Step 2

Factor $15 a^{2}$ out of $60 a^{3} - 75 a^{2}$ .

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Step 2.1

Factor $15 a^{2}$ out of $60 a^{3}$ .

$\frac{15 a^{2} (4 a) - 75 a^{2}}{15 a}$

Step 2.2

Factor $15 a^{2}$ out of $- 75 a^{2}$ .

$\frac{15 a^{2} (4 a) + 15 a^{2} (- 5)}{15 a}$

Step 2.3

Factor $15 a^{2}$ out of $15 a^{2} (4 a) + 15 a^{2} (- 5)$ .

$\frac{15 a^{2} (4 a - 5)}{15 a}$

$\frac{15 a^{2} (4 a - 5)}{15 a}$

Step 3

Cancel the common factor of $15$ .

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Step 3.1

Cancel the common factor.

$\frac{15 a^{2} (4 a - 5)}{15 a}$

Step 3.2

Rewrite the expression.

$\frac{a^{2} (4 a - 5)}{a}$

$\frac{a^{2} (4 a - 5)}{a}$

Step 4

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

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Step 4.1

Factor $a$ out of $a^{2} (4 a - 5)$ .

$\frac{a (a (4 a - 5))}{a}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

$\frac{a (a (4 a - 5))}{a^{1}}$

Step 4.2.2

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

$\frac{a (a (4 a - 5))}{a \cdot 1}$

Step 4.2.3

Cancel the common factor.

$\frac{a (a (4 a - 5))}{a \cdot 1}$

Step 4.2.4

Rewrite the expression.

$\frac{a (4 a - 5)}{1}$

Step 4.2.5

Divide $a (4 a - 5)$ by $1$ .

$a (4 a - 5)$

$a (4 a - 5)$

$a (4 a - 5)$

Step 5

Apply the distributive property.

$a (4 a) + a \cdot - 5$

Step 6

Rewrite using the commutative property of multiplication.

$4 a \cdot a + a \cdot - 5$

Step 7

Move $- 5$ to the left of $a$ .

$4 a \cdot a - 5 \cdot a$

Step 8

Multiply $a$ by $a$ by adding the exponents.

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Step 8.1

Move $a$ .

$4 (a \cdot a) - 5 \cdot a$

Step 8.2

Multiply $a$ by $a$ .

$4 a^{2} - 5 \cdot a$

$4 a^{2} - 5 a$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$