Basic Math Examples

$(- 5 y^{4} x^{3} + 27 y^{4} x^{7}) \div (- 3 y^{3} x^{4})$

Step 1

Rewrite the division as a fraction.

$\frac{- 5 y^{4} x^{3} + 27 y^{4} x^{7}}{- 3 y^{3} x^{4}}$

Step 2

Factor $y^{4} x^{3}$ out of $- 5 y^{4} x^{3} + 27 y^{4} x^{7}$ .

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Step 2.1

Factor $y^{4} x^{3}$ out of $- 5 y^{4} x^{3}$ .

$\frac{y^{4} x^{3} (- 5) + 27 y^{4} x^{7}}{- 3 y^{3} x^{4}}$

Step 2.2

Factor $y^{4} x^{3}$ out of $27 y^{4} x^{7}$ .

$\frac{y^{4} x^{3} (- 5) + y^{4} x^{3} (27 x^{4})}{- 3 y^{3} x^{4}}$

Step 2.3

Factor $y^{4} x^{3}$ out of $y^{4} x^{3} (- 5) + y^{4} x^{3} (27 x^{4})$ .

$\frac{y^{4} x^{3} (- 5 + 27 x^{4})}{- 3 y^{3} x^{4}}$

Step 3

Cancel the common factor of $y^{4}$ and $y^{3}$ .

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Step 3.1

Factor $y^{3}$ out of $y^{4} x^{3} (- 5 + 27 x^{4})$ .

$\frac{y^{3} (y x^{3} (- 5 + 27 x^{4}))}{- 3 y^{3} x^{4}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $y^{3}$ out of $- 3 y^{3} x^{4}$ .

$\frac{y^{3} (y x^{3} (- 5 + 27 x^{4}))}{y^{3} (- 3 x^{4})}$

Step 3.2.2

Cancel the common factor.

$\frac{y^{3} (y x^{3} (- 5 + 27 x^{4}))}{y^{3} (- 3 x^{4})}$

Step 3.2.3

Rewrite the expression.

$\frac{y x^{3} (- 5 + 27 x^{4})}{- 3 x^{4}}$

Step 4

Cancel the common factor of $x^{3}$ and $x^{4}$ .

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Step 4.1

Factor $x^{3}$ out of $y x^{3} (- 5 + 27 x^{4})$ .

$\frac{x^{3} (y (- 5 + 27 x^{4}))}{- 3 x^{4}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $x^{3}$ out of $- 3 x^{4}$ .

$\frac{x^{3} (y (- 5 + 27 x^{4}))}{x^{3} (- 3 x)}$

Step 4.2.2

Cancel the common factor.

$\frac{x^{3} (y (- 5 + 27 x^{4}))}{x^{3} (- 3 x)}$

Step 4.2.3

Rewrite the expression.

$\frac{y (- 5 + 27 x^{4})}{- 3 x}$

Step 5

Move the negative in front of the fraction.

$- \frac{y (- 5 + 27 x^{4})}{3 x}$

Step 6

Rewrite $- 5$ as $- 1 (5)$ .

$- \frac{y (- 1 (5) + 27 x^{4})}{3 x}$

Step 7

Factor $- 1$ out of $27 x^{4}$ .

$- \frac{y (- 1 (5) - (- 27 x^{4}))}{3 x}$

Step 8

Factor $- 1$ out of $- 1 (5) - (- 27 x^{4})$ .

$- \frac{y (- 1 (5 - 27 x^{4}))}{3 x}$

Step 9

Simplify the expression.

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Step 9.1

Move the negative in front of the fraction.

$- - \frac{y (5 - 27 x^{4})}{3 x}$

Step 9.2

Multiply $- 1$ by $- 1$ .

$1 \frac{y (5 - 27 x^{4})}{3 x}$

Step 9.3

Multiply $\frac{y (5 - 27 x^{4})}{3 x}$ by $1$ .

$\frac{y (5 - 27 x^{4})}{3 x}$