Basic Math Examples

$\frac{{(5 - a)}^{2}}{8 b^{2} c} \cdot \frac{4 a b}{4 (25 - a^{2})}$

Step 1

Simplify terms.

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Step 1.1

Combine.

$\frac{{(5 - a)}^{2} (4 a b)}{8 b^{2} c (4 (25 - a^{2}))}$

Step 1.2

Cancel the common factor of $4$ and $8$ .

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Step 1.2.1

Factor $4$ out of ${(5 - a)}^{2} (4 a b)$ .

$\frac{4 ({(5 - a)}^{2} (a b))}{8 b^{2} c (4 (25 - a^{2}))}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $4$ out of $8 b^{2} c (4 (25 - a^{2}))$ .

$\frac{4 ({(5 - a)}^{2} (a b))}{4 (2 b^{2} c (4 (25 - a^{2})))}$

Step 1.2.2.2

Cancel the common factor.

$\frac{4 ({(5 - a)}^{2} (a b))}{4 (2 b^{2} c (4 (25 - a^{2})))}$

Step 1.2.2.3

Rewrite the expression.

$\frac{{(5 - a)}^{2} (a b)}{2 b^{2} c (4 (25 - a^{2}))}$

Step 1.3

Cancel the common factor of $b$ and $b^{2}$ .

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Step 1.3.1

Factor $b$ out of ${(5 - a)}^{2} (a b)$ .

$\frac{b ({(5 - a)}^{2} (a))}{2 b^{2} c (4 (25 - a^{2}))}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $b$ out of $2 b^{2} c (4 (25 - a^{2}))$ .

$\frac{b ({(5 - a)}^{2} (a))}{b (2 b c (4 (25 - a^{2})))}$

Step 1.3.2.2

Cancel the common factor.

$\frac{b ({(5 - a)}^{2} (a))}{b (2 b c (4 (25 - a^{2})))}$

Step 1.3.2.3

Rewrite the expression.

$\frac{{(5 - a)}^{2} (a)}{2 b c (4 (25 - a^{2}))}$

Step 1.4

Multiply $4$ by $2$ .

$\frac{{(5 - a)}^{2} (a)}{8 b c (25 - a^{2})}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $25$ as $5^{2}$ .

$\frac{{(5 - a)}^{2} (a)}{8 b c (5^{2} - a^{2})}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 5$ and $b = a$ .

$\frac{{(5 - a)}^{2} (a)}{8 b c (5 + a) (5 - a)}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of ${(5 - a)}^{2}$ and $5 - a$ .

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Step 3.1.1

Factor $5 - a$ out of ${(5 - a)}^{2} (a)$ .

$\frac{(5 - a) ((5 - a) a)}{8 b c (5 + a) (5 - a)}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $5 - a$ out of $8 b c (5 + a) (5 - a)$ .

$\frac{(5 - a) ((5 - a) a)}{(5 - a) (8 b c (5 + a))}$

Step 3.1.2.2

Cancel the common factor.

$\frac{(5 - a) ((5 - a) a)}{(5 - a) (8 b c (5 + a))}$

Step 3.1.2.3

Rewrite the expression.

$\frac{(5 - a) a}{8 b c (5 + a)}$

Step 3.2

Reorder factors in $\frac{(5 - a) a}{8 b c (5 + a)}$ .

$\frac{a (5 - a)}{8 b c (5 + a)}$