Simplify (14a^8y^3-7a^4y^5+28a^12y^2)/(7a^4y)

$\frac{14 a^{8} y^{3} - 7 a^{4} y^{5} + 28 a^{12} y^{2}}{7 a^{4} y}$

Step 1

Simplify the numerator.

Factor $7 a^{4} y^{2}$ out of $14 a^{8} y^{3} - 7 a^{4} y^{5} + 28 a^{12} y^{2}$ .

Factor $7 a^{4} y^{2}$ out of $14 a^{8} y^{3}$ .

$\frac{7 a^{4} y^{2} (2 a^{4} y) - 7 a^{4} y^{5} + 28 a^{12} y^{2}}{7 a^{4} y}$

Factor $7 a^{4} y^{2}$ out of $- 7 a^{4} y^{5}$ .

$\frac{7 a^{4} y^{2} (2 a^{4} y) + 7 a^{4} y^{2} (- 1 y^{3}) + 28 a^{12} y^{2}}{7 a^{4} y}$

Factor $7 a^{4} y^{2}$ out of $28 a^{12} y^{2}$ .

$\frac{7 a^{4} y^{2} (2 a^{4} y) + 7 a^{4} y^{2} (- 1 y^{3}) + 7 a^{4} y^{2} (4 a^{8})}{7 a^{4} y}$

Factor $7 a^{4} y^{2}$ out of $7 a^{4} y^{2} (2 a^{4} y) + 7 a^{4} y^{2} (- 1 y^{3})$ .

$\frac{7 a^{4} y^{2} (2 a^{4} y - 1 y^{3}) + 7 a^{4} y^{2} (4 a^{8})}{7 a^{4} y}$

Factor $7 a^{4} y^{2}$ out of $7 a^{4} y^{2} (2 a^{4} y - 1 y^{3}) + 7 a^{4} y^{2} (4 a^{8})$ .

$\frac{7 a^{4} y^{2} (2 a^{4} y - 1 y^{3} + 4 a^{8})}{7 a^{4} y}$

Rewrite $- 1 y^{3}$ as $- y^{3}$ .

$\frac{7 a^{4} y^{2} (2 a^{4} y - y^{3} + 4 a^{8})}{7 a^{4} y}$

Step 2

Simplify terms.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 a^{4} y^{2} (2 a^{4} y - y^{3} + 4 a^{8})}{7 a^{4} y}$

Rewrite the expression.

$\frac{a^{4} y^{2} (2 a^{4} y - y^{3} + 4 a^{8})}{a^{4} y}$

Cancel the common factor of $a^{4}$ .

Cancel the common factor.

$\frac{a^{4} y^{2} (2 a^{4} y - y^{3} + 4 a^{8})}{a^{4} y}$

Rewrite the expression.

$\frac{y^{2} (2 a^{4} y - y^{3} + 4 a^{8})}{y}$

Cancel the common factor of $y^{2}$ and $y$ .

Factor $y$ out of $y^{2} (2 a^{4} y - y^{3} + 4 a^{8})$ .

$\frac{y (y (2 a^{4} y - y^{3} + 4 a^{8}))}{y}$

Cancel the common factors.

Raise $y$ to the power of $1$ .

$\frac{y (y (2 a^{4} y - y^{3} + 4 a^{8}))}{y^{1}}$

Factor $y$ out of $y^{1}$ .

$\frac{y (y (2 a^{4} y - y^{3} + 4 a^{8}))}{y \cdot 1}$

Cancel the common factor.

$\frac{y (y (2 a^{4} y - y^{3} + 4 a^{8}))}{y \cdot 1}$

Rewrite the expression.

$\frac{y (2 a^{4} y - y^{3} + 4 a^{8})}{1}$

Divide $y (2 a^{4} y - y^{3} + 4 a^{8})$ by $1$ .

$y (2 a^{4} y - y^{3} + 4 a^{8})$

Apply the distributive property.

$y (2 a^{4} y) + y (- y^{3}) + y (4 a^{8})$

Step 3

Simplify.

Rewrite using the commutative property of multiplication.

$2 y (a^{4} y) + y (- y^{3}) + y (4 a^{8})$

Rewrite using the commutative property of multiplication.

$2 y (a^{4} y) - y \cdot y^{3} + y (4 a^{8})$

Rewrite using the commutative property of multiplication.

$2 y (a^{4} y) - y \cdot y^{3} + 4 y a^{8}$

Step 4

Simplify each term.

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$2 (y \cdot y) a^{4} - y \cdot y^{3} + 4 y a^{8}$

Multiply $y$ by $y$ .

$2 y^{2} a^{4} - y \cdot y^{3} + 4 y a^{8}$

Multiply $y$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

$2 y^{2} a^{4} - (y^{3} y) + 4 y a^{8}$

Multiply $y^{3}$ by $y$ .

Raise $y$ to the power of $1$ .

$2 y^{2} a^{4} - (y^{3} y^{1}) + 4 y a^{8}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 y^{2} a^{4} - y^{3 + 1} + 4 y a^{8}$

Add $3$ and $1$ .

$2 y^{2} a^{4} - y^{4} + 4 y a^{8}$

Step 5

Simplify the expression.

Move $y^{2}$ .

$2 a^{4} y^{2} - y^{4} + 4 y a^{8}$

Move $y$ .

$2 a^{4} y^{2} - y^{4} + 4 a^{8} y$

Move $- y^{4}$ .

$2 a^{4} y^{2} + 4 a^{8} y - y^{4}$

Reorder $2 a^{4} y^{2}$ and $4 a^{8} y$ .

$4 a^{8} y + 2 a^{4} y^{2} - y^{4}$

Simplify (14a^8y^3-7a^4y^5+28a^12y^2)/(7a^4y)

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