Algebra Examples

$\frac{2 \cdot 4^{2} - 8 \div 2}{(5 + 2) \cdot 2}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Cancel the common factor of $8$ and $2$ .

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Step 1.1.1

Factor $2$ out of $8$ .

$\frac{2 \cdot 4^{2} - 2 \cdot 4 \div 2}{(5 + 2) \cdot 2}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $2$ .

$\frac{2 \cdot 4^{2} - 2 \cdot 4 \div 2 (1)}{(5 + 2) \cdot 2}$

Step 1.1.2.2

Cancel the common factor.

$\frac{2 \cdot 4^{2} - 2 \cdot 4 \div 2 \cdot 1}{(5 + 2) \cdot 2}$

Step 1.1.2.3

Rewrite the expression.

$\frac{2 \cdot 4^{2} - \frac{4}{1}}{(5 + 2) \cdot 2}$

Step 1.1.2.4

Divide $4$ by $1$ .

$\frac{2 \cdot 4^{2} - 1 \cdot 4}{(5 + 2) \cdot 2}$

Step 1.2

Cancel the common factor of $2 \cdot 4^{2} - 1 \cdot 4$ and $2$ .

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Step 1.2.1

Factor $2$ out of $2 \cdot 4^{2}$ .

$\frac{2 (4^{2}) - 1 \cdot 4}{(5 + 2) \cdot 2}$

Step 1.2.2

Factor $2$ out of $- 1 \cdot 4$ .

$\frac{2 (4^{2}) + 2 (- 1 \cdot 2)}{(5 + 2) \cdot 2}$

Step 1.2.3

Factor $2$ out of $2 (4^{2}) + 2 (- 1 \cdot 2)$ .

$\frac{2 (4^{2} - 1 \cdot 2)}{(5 + 2) \cdot 2}$

Step 1.2.4

Cancel the common factors.

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Step 1.2.4.1

Factor $2$ out of $(5 + 2) \cdot 2$ .

$\frac{2 (4^{2} - 1 \cdot 2)}{2 \cdot (5 + 2)}$

Step 1.2.4.2

Cancel the common factor.

$\frac{2 (4^{2} - 1 \cdot 2)}{2 \cdot (5 + 2)}$

Step 1.2.4.3

Rewrite the expression.

$\frac{4^{2} - 1 \cdot 2}{5 + 2}$

Step 2

Simplify the numerator.

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Step 2.1

Raise $4$ to the power of $2$ .

$\frac{16 - 1 \cdot 2}{5 + 2}$

Step 2.2

Multiply $- 1$ by $2$ .

$\frac{16 - 2}{5 + 2}$

Step 2.3

Subtract $2$ from $16$ .

$\frac{14}{5 + 2}$

Step 3

Simplify the expression.

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Step 3.1

Add $5$ and $2$ .

$\frac{14}{7}$

Step 3.2

Divide $14$ by $7$ .

$2$