Algebra Examples

$12 + (2 - (4 \cdot a^{2})) \div 7 + b$

Step 1

Simplify each term.

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Step 1.1

Rewrite the division as a fraction.

$12 + \frac{2 - (4 \cdot a^{2})}{7} + b$

Step 1.2

Simplify the numerator.

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Step 1.2.1

Multiply $- 1$ by $4$ .

$12 + \frac{2 - 4 \cdot a^{2}}{7} + b$

Step 1.2.2

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

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Step 1.2.2.1

Factor $2$ out of $2$ .

$12 + \frac{2 (1) - 4 a^{2}}{7} + b$

Step 1.2.2.2

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

$12 + \frac{2 (1) + 2 (- 2 a^{2})}{7} + b$

Step 1.2.2.3

Factor $2$ out of $2 (1) + 2 (- 2 a^{2})$ .

$12 + \frac{2 (1 - 2 a^{2})}{7} + b$

Step 2

To write $12$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$12 \cdot \frac{7}{7} + \frac{2 (1 - 2 a^{2})}{7} + b$

Step 3

Simplify terms.

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Step 3.1

Combine $12$ and $\frac{7}{7}$ .

$\frac{12 \cdot 7}{7} + \frac{2 (1 - 2 a^{2})}{7} + b$

Step 3.2

Combine the numerators over the common denominator.

$\frac{12 \cdot 7 + 2 (1 - 2 a^{2})}{7} + b$

Step 3.3

Multiply $12$ by $7$ .

$\frac{84 + 2 (1 - 2 a^{2})}{7} + b$

Step 4

Simplify the numerator.

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Step 4.1

Factor $2$ out of $84 + 2 (1 - 2 a^{2})$ .

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Step 4.1.1

Factor $2$ out of $84$ .

$\frac{2 \cdot 42 + 2 (1 - 2 a^{2})}{7} + b$

Step 4.1.2

Factor $2$ out of $2 \cdot 42 + 2 (1 - 2 a^{2})$ .

$\frac{2 (42 + 1 - 2 a^{2})}{7} + b$

Step 4.2

Add $42$ and $1$ .

$\frac{2 (43 - 2 a^{2})}{7} + b$

Step 5

To write $b$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{2 (43 - 2 a^{2})}{7} + b \cdot \frac{7}{7}$

Step 6

Simplify terms.

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Step 6.1

Combine $b$ and $\frac{7}{7}$ .

$\frac{2 (43 - 2 a^{2})}{7} + \frac{b \cdot 7}{7}$

Step 6.2

Combine the numerators over the common denominator.

$\frac{2 (43 - 2 a^{2}) + b \cdot 7}{7}$

Step 7

Simplify the numerator.

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Step 7.1

Apply the distributive property.

$\frac{2 \cdot 43 + 2 (- 2 a^{2}) + b \cdot 7}{7}$

Step 7.2

Multiply $2$ by $43$ .

$\frac{86 + 2 (- 2 a^{2}) + b \cdot 7}{7}$

Step 7.3

Multiply $- 2$ by $2$ .

$\frac{86 - 4 a^{2} + b \cdot 7}{7}$

Step 7.4

Move $7$ to the left of $b$ .

$\frac{86 - 4 a^{2} + 7 b}{7}$