Simplify (31y^4z^7-28y^7z^7)÷(-4y^5z^4)

$(31 y^{4} z^{7} - 28 y^{7} z^{7}) \div (- 4 y^{5} z^{4})$

Step 1

Rewrite the division as a fraction.

$\frac{31 y^{4} z^{7} - 28 y^{7} z^{7}}{- 4 y^{5} z^{4}}$

Step 2

Factor $y^{4} z^{7}$ out of $31 y^{4} z^{7} - 28 y^{7} z^{7}$ .

Factor $y^{4} z^{7}$ out of $31 y^{4} z^{7}$ .

$\frac{y^{4} z^{7} (31) - 28 y^{7} z^{7}}{- 4 y^{5} z^{4}}$

Factor $y^{4} z^{7}$ out of $- 28 y^{7} z^{7}$ .

$\frac{y^{4} z^{7} (31) + y^{4} z^{7} (- 28 y^{3})}{- 4 y^{5} z^{4}}$

Factor $y^{4} z^{7}$ out of $y^{4} z^{7} (31) + y^{4} z^{7} (- 28 y^{3})$ .

$\frac{y^{4} z^{7} (31 - 28 y^{3})}{- 4 y^{5} z^{4}}$

Step 3

Cancel the common factor of $y^{4}$ and $y^{5}$ .

Factor $y^{4}$ out of $y^{4} z^{7} (31 - 28 y^{3})$ .

$\frac{y^{4} (z^{7} (31 - 28 y^{3}))}{- 4 y^{5} z^{4}}$

Cancel the common factors.

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

$\frac{y^{4} (z^{7} (31 - 28 y^{3}))}{y^{4} (- 4 y z^{4})}$

Cancel the common factor.

$\frac{y^{4} (z^{7} (31 - 28 y^{3}))}{y^{4} (- 4 y z^{4})}$

Rewrite the expression.

$\frac{z^{7} (31 - 28 y^{3})}{- 4 y z^{4}}$

Step 4

Cancel the common factor of $z^{7}$ and $z^{4}$ .

Factor $z^{4}$ out of $z^{7} (31 - 28 y^{3})$ .

$\frac{z^{4} (z^{3} (31 - 28 y^{3}))}{- 4 y z^{4}}$

Cancel the common factors.

Factor $z^{4}$ out of $- 4 y z^{4}$ .

$\frac{z^{4} (z^{3} (31 - 28 y^{3}))}{z^{4} (- 4 y)}$

Cancel the common factor.

$\frac{z^{4} (z^{3} (31 - 28 y^{3}))}{z^{4} (- 4 y)}$

Rewrite the expression.

$\frac{z^{3} (31 - 28 y^{3})}{- 4 y}$

Step 5

Move the negative in front of the fraction.

$- \frac{z^{3} (31 - 28 y^{3})}{4 y}$