Algebra Examples

${(24 \div 8 + (12 - 3) \div 6)}^{2}$

Step 1

Subtract $3$ from $12$ .

${(24 \div 8 + 9 \div 6)}^{2}$

Step 2

Simplify each term.

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Step 2.1

Divide $24$ by $8$ .

${(3 + 9 \div 6)}^{2}$

Step 2.2

Rewrite the division as a fraction.

${(3 + \frac{9}{6})}^{2}$

Step 2.3

Cancel the common factor of $9$ and $6$ .

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Step 2.3.1

Factor $3$ out of $9$ .

${(3 + \frac{3 (3)}{6})}^{2}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $3$ out of $6$ .

${(3 + \frac{3 \cdot 3}{3 \cdot 2})}^{2}$

Step 2.3.2.2

Cancel the common factor.

${(3 + \frac{3 \cdot 3}{3 \cdot 2})}^{2}$

Step 2.3.2.3

Rewrite the expression.

${(3 + \frac{3}{2})}^{2}$

Step 3

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

${(3 \cdot \frac{2}{2} + \frac{3}{2})}^{2}$

Step 4

Combine $3$ and $\frac{2}{2}$ .

${(\frac{3 \cdot 2}{2} + \frac{3}{2})}^{2}$

Step 5

Combine the numerators over the common denominator.

${(\frac{3 \cdot 2 + 3}{2})}^{2}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $3$ by $2$ .

${(\frac{6 + 3}{2})}^{2}$

Step 6.2

Add $6$ and $3$ .

${(\frac{9}{2})}^{2}$

Step 7

Apply the product rule to $\frac{9}{2}$ .

$\frac{9^{2}}{2^{2}}$

Step 8

Raise $9$ to the power of $2$ .

$\frac{81}{2^{2}}$

Step 9

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

$\frac{81}{4}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{81}{4}$

Decimal Form:

$20.25$

Mixed Number Form:

$20 \frac{1}{4}$