Basic Math Examples

$\frac{24 z^{5} - 16 z^{4}}{4 z^{2}}$

Step 1

Simplify terms.

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Step 1.1

Factor $8 z^{4}$ out of $24 z^{5} - 16 z^{4}$ .

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Step 1.1.1

Factor $8 z^{4}$ out of $24 z^{5}$ .

$\frac{8 z^{4} (3 z) - 16 z^{4}}{4 z^{2}}$

Step 1.1.2

Factor $8 z^{4}$ out of $- 16 z^{4}$ .

$\frac{8 z^{4} (3 z) + 8 z^{4} (- 2)}{4 z^{2}}$

Step 1.1.3

Factor $8 z^{4}$ out of $8 z^{4} (3 z) + 8 z^{4} (- 2)$ .

$\frac{8 z^{4} (3 z - 2)}{4 z^{2}}$

$\frac{8 z^{4} (3 z - 2)}{4 z^{2}}$

Step 1.2

Cancel the common factor of $8$ and $4$ .

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Step 1.2.1

Factor $4$ out of $8 z^{4} (3 z - 2)$ .

$\frac{4 (2 z^{4} (3 z - 2))}{4 z^{2}}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $4$ out of $4 z^{2}$ .

$\frac{4 (2 z^{4} (3 z - 2))}{4 (z^{2})}$

Step 1.2.2.2

Cancel the common factor.

$\frac{4 (2 z^{4} (3 z - 2))}{4 z^{2}}$

Step 1.2.2.3

Rewrite the expression.

$\frac{2 z^{4} (3 z - 2)}{z^{2}}$

$\frac{2 z^{4} (3 z - 2)}{z^{2}}$

$\frac{2 z^{4} (3 z - 2)}{z^{2}}$

Step 1.3

Cancel the common factor of $z^{4}$ and $z^{2}$ .

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Step 1.3.1

Factor $z^{2}$ out of $2 z^{4} (3 z - 2)$ .

$\frac{z^{2} (2 z^{2} (3 z - 2))}{z^{2}}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Multiply by $1$ .

$\frac{z^{2} (2 z^{2} (3 z - 2))}{z^{2} \cdot 1}$

Step 1.3.2.2

Cancel the common factor.

$\frac{z^{2} (2 z^{2} (3 z - 2))}{z^{2} \cdot 1}$

Step 1.3.2.3

Rewrite the expression.

$\frac{2 z^{2} (3 z - 2)}{1}$

Step 1.3.2.4

Divide $2 z^{2} (3 z - 2)$ by $1$ .

$2 z^{2} (3 z - 2)$

$2 z^{2} (3 z - 2)$

$2 z^{2} (3 z - 2)$

Step 1.4

Apply the distributive property.

$2 z^{2} (3 z) + 2 z^{2} \cdot - 2$

Step 1.5

Simplify the expression.

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Step 1.5.1

Rewrite using the commutative property of multiplication.

$2 \cdot 3 z^{2} z + 2 z^{2} \cdot - 2$

Step 1.5.2

Multiply $- 2$ by $2$ .

$2 \cdot 3 z^{2} z - 4 z^{2}$

$2 \cdot 3 z^{2} z - 4 z^{2}$

$2 \cdot 3 z^{2} z - 4 z^{2}$

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

Move $z$ .

$2 \cdot 3 (z \cdot z^{2}) - 4 z^{2}$

Step 2.1.2

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

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Step 2.1.2.1

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

$2 \cdot 3 (z^{1} z^{2}) - 4 z^{2}$

Step 2.1.2.2

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

$2 \cdot 3 z^{1 + 2} - 4 z^{2}$

$2 \cdot 3 z^{1 + 2} - 4 z^{2}$

Step 2.1.3

Add $1$ and $2$ .

$2 \cdot 3 z^{3} - 4 z^{2}$

$2 \cdot 3 z^{3} - 4 z^{2}$

Step 2.2

Multiply $2$ by $3$ .

$6 z^{3} - 4 z^{2}$

$6 z^{3} - 4 z^{2}$

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