Pre-Algebra Examples

$\frac{21 x^{2} + 28 x}{3}$

Step 1

Factor $7 x$ out of $21 x^{2} + 28 x$ .

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Step 1.1

Factor $7 x$ out of $21 x^{2}$ .

$\frac{7 x (3 x) + 28 x}{3}$

Step 1.2

Factor $7 x$ out of $28 x$ .

$\frac{7 x (3 x) + 7 x (4)}{3}$

Step 1.3

Factor $7 x$ out of $7 x (3 x) + 7 x (4)$ .

$\frac{7 x (3 x + 4)}{3}$

$\frac{7 x (3 x + 4)}{3}$

Step 2

Apply the distributive property.

$\frac{7 x (3 x) + 7 x \cdot 4}{3}$

Step 3

Rewrite using the commutative property of multiplication.

$\frac{7 \cdot 3 x \cdot x + 7 x \cdot 4}{3}$

Step 4

Multiply $4$ by $7$ .

$\frac{7 \cdot 3 x \cdot x + 28 x}{3}$

Step 5

Simplify each term.

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Step 5.1

Multiply $x$ by $x$ by adding the exponents.

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Step 5.1.1

Move $x$ .

$\frac{7 \cdot 3 (x \cdot x) + 28 x}{3}$

Step 5.1.2

Multiply $x$ by $x$ .

$\frac{7 \cdot 3 x^{2} + 28 x}{3}$

$\frac{7 \cdot 3 x^{2} + 28 x}{3}$

Step 5.2

Multiply $7$ by $3$ .

$\frac{21 x^{2} + 28 x}{3}$

$\frac{21 x^{2} + 28 x}{3}$

Step 6

Split the fraction $\frac{21 x^{2} + 28 x}{3}$ into two fractions.

$\frac{21 x^{2}}{3} + \frac{28 x}{3}$

Step 7

Cancel the common factor of $21$ and $3$ .

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Step 7.1

Factor $3$ out of $21 x^{2}$ .

$\frac{3 (7 x^{2})}{3} + \frac{28 x}{3}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $3$ out of $3$ .

$\frac{3 (7 x^{2})}{3 (1)} + \frac{28 x}{3}$

Step 7.2.2

Cancel the common factor.

$\frac{3 (7 x^{2})}{3 \cdot 1} + \frac{28 x}{3}$

Step 7.2.3

Rewrite the expression.

$\frac{7 x^{2}}{1} + \frac{28 x}{3}$

Step 7.2.4

Divide $7 x^{2}$ by $1$ .

$7 x^{2} + \frac{28 x}{3}$

$7 x^{2} + \frac{28 x}{3}$

$7 x^{2} + \frac{28 x}{3}$

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