Pre-Algebra Examples

$(14 x^{2} - 14 x^{4} - 35 x^{2}) \div (- 7 x^{2})$

Step 1

Rewrite the division as a fraction.

$\frac{14 x^{2} - 14 x^{4} - 35 x^{2}}{- 7 x^{2}}$

Step 2

Simplify the numerator.

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Step 2.1

Subtract $35 x^{2}$ from $14 x^{2}$ .

$\frac{- 14 x^{4} - 21 x^{2}}{- 7 x^{2}}$

Step 2.2

Factor $7 x^{2}$ out of $- 14 x^{4} - 21 x^{2}$ .

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Step 2.2.1

Factor $7 x^{2}$ out of $- 14 x^{4}$ .

$\frac{7 x^{2} (- 2 x^{2}) - 21 x^{2}}{- 7 x^{2}}$

Step 2.2.2

Factor $7 x^{2}$ out of $- 21 x^{2}$ .

$\frac{7 x^{2} (- 2 x^{2}) + 7 x^{2} (- 3)}{- 7 x^{2}}$

Step 2.2.3

Factor $7 x^{2}$ out of $7 x^{2} (- 2 x^{2}) + 7 x^{2} (- 3)$ .

$\frac{7 x^{2} (- 2 x^{2} - 3)}{- 7 x^{2}}$

Step 3

Cancel the common factor of $7$ and $- 7$ .

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Step 3.1

Factor $7$ out of $7 x^{2} (- 2 x^{2} - 3)$ .

$\frac{7 (x^{2} (- 2 x^{2} - 3))}{- 7 x^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $7$ out of $- 7 x^{2}$ .

$\frac{7 (x^{2} (- 2 x^{2} - 3))}{7 (- x^{2})}$

Step 3.2.2

Cancel the common factor.

$\frac{7 (x^{2} (- 2 x^{2} - 3))}{7 (- x^{2})}$

Step 3.2.3

Rewrite the expression.

$\frac{x^{2} (- 2 x^{2} - 3)}{- x^{2}}$

Step 4

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

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Step 4.1

Cancel the common factor.

$\frac{x^{2} (- 2 x^{2} - 3)}{- x^{2}}$

Step 4.2

Rewrite the expression.

$\frac{- 2 x^{2} - 3}{- 1}$

Step 4.3

Move the negative one from the denominator of $\frac{- 2 x^{2} - 3}{- 1}$ .

$- 1 \cdot (- 2 x^{2} - 3)$

Step 5

Rewrite $- 1 \cdot (- 2 x^{2} - 3)$ as $- (- 2 x^{2} - 3)$ .

$- (- 2 x^{2} - 3)$

Step 6

Apply the distributive property.

$- (- 2 x^{2}) - - 3$

Step 7

Multiply $- 2$ by $- 1$ .

$2 x^{2} - - 3$

Step 8

Multiply $- 1$ by $- 3$ .

$2 x^{2} + 3$