Basic Math Examples

$(5 - a) (5 - b) (5 - c) (5 - d) = 25$

Step 1

Divide each term in $(5 - a) (5 - b) (5 - c) (5 - d) = 25$ by $(5 - b) (5 - c) (5 - d)$ and simplify.

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Step 1.1

Divide each term in $(5 - a) (5 - b) (5 - c) (5 - d) = 25$ by $(5 - b) (5 - c) (5 - d)$ .

$\frac{(5 - a) (5 - b) (5 - c) (5 - d)}{(5 - b) (5 - c) (5 - d)} = \frac{25}{(5 - b) (5 - c) (5 - d)}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $5 - b$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{(5 - a) (5 - b) (5 - c) (5 - d)}{(5 - b) (5 - c) (5 - d)} = \frac{25}{(5 - b) (5 - c) (5 - d)}$

Step 1.2.1.2

Rewrite the expression.

$\frac{((5 - a) (5 - c)) (5 - d)}{(5 - c) (5 - d)} = \frac{25}{(5 - b) (5 - c) (5 - d)}$

Step 1.2.2

Cancel the common factor of $5 - c$ .

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Step 1.2.2.1

Cancel the common factor.

$\frac{(5 - a) (5 - c) (5 - d)}{(5 - c) (5 - d)} = \frac{25}{(5 - b) (5 - c) (5 - d)}$

Step 1.2.2.2

Rewrite the expression.

$\frac{(5 - a) (5 - d)}{5 - d} = \frac{25}{(5 - b) (5 - c) (5 - d)}$

Step 1.2.3

Cancel the common factor of $5 - d$ .

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Step 1.2.3.1

Cancel the common factor.

$\frac{(5 - a) (5 - d)}{5 - d} = \frac{25}{(5 - b) (5 - c) (5 - d)}$

Step 1.2.3.2

Divide $5 - a$ by $1$ .

$5 - a = \frac{25}{(5 - b) (5 - c) (5 - d)}$

Step 2

Subtract $5$ from both sides of the equation.

$- a = \frac{25}{(5 - b) (5 - c) (5 - d)} - 5$

Step 3

Divide each term in $- a = \frac{25}{(5 - b) (5 - c) (5 - d)} - 5$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- a = \frac{25}{(5 - b) (5 - c) (5 - d)} - 5$ by $- 1$ .

$\frac{- a}{- 1} = \frac{\frac{25}{(5 - b) (5 - c) (5 - d)}}{- 1} + \frac{- 5}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{a}{1} = \frac{\frac{25}{(5 - b) (5 - c) (5 - d)}}{- 1} + \frac{- 5}{- 1}$

Step 3.2.2

Divide $a$ by $1$ .

$a = \frac{\frac{25}{(5 - b) (5 - c) (5 - d)}}{- 1} + \frac{- 5}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Move the negative one from the denominator of $\frac{\frac{25}{(5 - b) (5 - c) (5 - d)}}{- 1}$ .

$a = - 1 \cdot \frac{25}{(5 - b) (5 - c) (5 - d)} + \frac{- 5}{- 1}$

Step 3.3.1.2

Rewrite $- 1 \cdot \frac{25}{(5 - b) (5 - c) (5 - d)}$ as $- \frac{25}{(5 - b) (5 - c) (5 - d)}$ .

$a = - \frac{25}{(5 - b) (5 - c) (5 - d)} + \frac{- 5}{- 1}$

Step 3.3.1.3

Divide $- 5$ by $- 1$ .

$a = - \frac{25}{(5 - b) (5 - c) (5 - d)} + 5$