Basic Math Examples

$7 a - 14 b \div 2 (a - 2 b)$

Step 1

Simplify each term.

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Step 1.1

Rewrite the division as a fraction.

$7 a - \frac{14 b}{2 (a - 2 b)}$

Step 1.2

Cancel the common factor of $14$ and $2$ .

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Step 1.2.1

Factor $2$ out of $14 b$ .

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

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Cancel the common factor.

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

Step 1.2.2.2

Rewrite the expression.

$7 a - \frac{7 b}{a - 2 b}$

Step 2

To write $7 a$ as a fraction with a common denominator, multiply by $\frac{a - 2 b}{a - 2 b}$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

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Step 4.1

Factor $7$ out of $7 a (a - 2 b) - 7 b$ .

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Step 4.1.1

Factor $7$ out of $7 a (a - 2 b)$ .

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

Step 4.1.2

Factor $7$ out of $- 7 b$ .

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

Step 4.1.3

Factor $7$ out of $7 (a (a - 2 b)) + 7 (- b)$ .

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

Step 4.2

Apply the distributive property.

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

Step 4.3

Multiply $a$ by $a$ .

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

Step 4.4

Rewrite using the commutative property of multiplication.

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