Pre-Algebra Examples

$(90 x^{6} + 63 x^{4} - 18 x^{2}) \div {(9 x)}^{2}$

Step 1

Rewrite the division as a fraction.

$\frac{90 x^{6} + 63 x^{4} - 18 x^{2}}{{(9 x)}^{2}}$

Step 2

Factor $9 x^{2}$ out of $90 x^{6} + 63 x^{4} - 18 x^{2}$ .

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Step 2.1

Factor $9 x^{2}$ out of $90 x^{6}$ .

$\frac{9 x^{2} (10 x^{4}) + 63 x^{4} - 18 x^{2}}{{(9 x)}^{2}}$

Step 2.2

Factor $9 x^{2}$ out of $63 x^{4}$ .

$\frac{9 x^{2} (10 x^{4}) + 9 x^{2} (7 x^{2}) - 18 x^{2}}{{(9 x)}^{2}}$

Step 2.3

Factor $9 x^{2}$ out of $- 18 x^{2}$ .

$\frac{9 x^{2} (10 x^{4}) + 9 x^{2} (7 x^{2}) + 9 x^{2} (- 2)}{{(9 x)}^{2}}$

Step 2.4

Factor $9 x^{2}$ out of $9 x^{2} (10 x^{4}) + 9 x^{2} (7 x^{2})$ .

$\frac{9 x^{2} (10 x^{4} + 7 x^{2}) + 9 x^{2} (- 2)}{{(9 x)}^{2}}$

Step 2.5

Factor $9 x^{2}$ out of $9 x^{2} (10 x^{4} + 7 x^{2}) + 9 x^{2} (- 2)$ .

$\frac{9 x^{2} (10 x^{4} + 7 x^{2} - 2)}{{(9 x)}^{2}}$

Step 3

Simplify the denominator.

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Step 3.1

Apply the product rule to $9 x$ .

$\frac{9 x^{2} (10 x^{4} + 7 x^{2} - 2)}{9^{2} x^{2}}$

Step 3.2

Raise $9$ to the power of $2$ .

$\frac{9 x^{2} (10 x^{4} + 7 x^{2} - 2)}{81 x^{2}}$

Step 4

Cancel the common factor of $9$ and $81$ .

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Step 4.1

Factor $9$ out of $9 x^{2} (10 x^{4} + 7 x^{2} - 2)$ .

$\frac{9 (x^{2} (10 x^{4} + 7 x^{2} - 2))}{81 x^{2}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $9$ out of $81 x^{2}$ .

$\frac{9 (x^{2} (10 x^{4} + 7 x^{2} - 2))}{9 (9 x^{2})}$

Step 4.2.2

Cancel the common factor.

$\frac{9 (x^{2} (10 x^{4} + 7 x^{2} - 2))}{9 (9 x^{2})}$

Step 4.2.3

Rewrite the expression.

$\frac{x^{2} (10 x^{4} + 7 x^{2} - 2)}{9 x^{2}}$

Step 5

Cancel the common factor of $x^{2}$ .

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Step 5.1

Cancel the common factor.

$\frac{x^{2} (10 x^{4} + 7 x^{2} - 2)}{9 x^{2}}$

Step 5.2

Rewrite the expression.

$\frac{10 x^{4} + 7 x^{2} - 2}{9}$

Step 6

Split the fraction $\frac{10 x^{4} + 7 x^{2} - 2}{9}$ into two fractions.

$\frac{10 x^{4} + 7 x^{2}}{9} + \frac{- 2}{9}$

Step 7

Split the fraction $\frac{10 x^{4} + 7 x^{2}}{9}$ into two fractions.

$\frac{10 x^{4}}{9} + \frac{7 x^{2}}{9} + \frac{- 2}{9}$

Step 8

Move the negative in front of the fraction.

$\frac{10 x^{4}}{9} + \frac{7 x^{2}}{9} - \frac{2}{9}$