Basic Math Examples

$\frac{7 a^{2}}{7 a^{3} + 56^{2}} \cdot \frac{a^{2} + 7 a - 8}{2}$

Step 1

Simplify the denominator.

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Step 1.1

Raise $56$ to the power of $2$ .

$\frac{7 a^{2}}{7 a^{3} + 3136} \cdot \frac{a^{2} + 7 a - 8}{2}$

Step 1.2

Factor $7$ out of $7 a^{3} + 3136$ .

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Step 1.2.1

Factor $7$ out of $7 a^{3}$ .

$\frac{7 a^{2}}{7 (a^{3}) + 3136} \cdot \frac{a^{2} + 7 a - 8}{2}$

Step 1.2.2

Factor $7$ out of $3136$ .

$\frac{7 a^{2}}{7 a^{3} + 7 \cdot 448} \cdot \frac{a^{2} + 7 a - 8}{2}$

Step 1.2.3

Factor $7$ out of $7 a^{3} + 7 \cdot 448$ .

$\frac{7 a^{2}}{7 (a^{3} + 448)} \cdot \frac{a^{2} + 7 a - 8}{2}$

Step 2

Factor $a^{2} + 7 a - 8$ using the AC method.

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Step 2.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 8$ and whose sum is $7$ .

$- 1, 8$

Step 2.2

Write the factored form using these integers.

$\frac{7 a^{2}}{7 (a^{3} + 448)} \cdot \frac{(a - 1) (a + 8)}{2}$

Step 3

Simplify terms.

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Step 3.1

Combine.

$\frac{7 a^{2} ((a - 1) (a + 8))}{7 (a^{3} + 448) \cdot 2}$

Step 3.2

Cancel the common factor of $7$ .

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Step 3.2.1

Cancel the common factor.

$\frac{7 a^{2} ((a - 1) (a + 8))}{7 (a^{3} + 448) \cdot 2}$

Step 3.2.2

Rewrite the expression.

$\frac{a^{2} ((a - 1) (a + 8))}{(a^{3} + 448) \cdot 2}$

Step 4

Simplify the numerator.

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Step 4.1

Rewrite.

$\frac{7 a^{2} ((a - 1) (a + 8))}{(a^{3} + 448) \cdot 2}$

Step 4.2

Rewrite.

$\frac{a^{2} ((a - 1) (a + 8))}{(a^{3} + 448) \cdot 2}$

Step 4.3

Remove unnecessary parentheses.

$\frac{a^{2} (a - 1) (a + 8)}{(a^{3} + 448) \cdot 2}$

Step 5

Move $2$ to the left of $a^{3} + 448$ .

$\frac{a^{2} (a - 1) (a + 8)}{2 (a^{3} + 448)}$