Simplify (32a^8b^6-12a^5b^4c^2)/(4a^3b^3)

$\frac{32 a^{8} b^{6} - 12 a^{5} b^{4} c^{2}}{4 a^{3} b^{3}}$

Simplify terms.

Factor $4 a^{5} b^{4}$ out of $32 a^{8} b^{6} - 12 a^{5} b^{4} c^{2}$ .

Factor $4 a^{5} b^{4}$ out of $32 a^{8} b^{6}$ .

$\frac{4 a^{5} b^{4} (8 a^{3} b^{2}) - 12 a^{5} b^{4} c^{2}}{4 a^{3} b^{3}}$

Factor $4 a^{5} b^{4}$ out of $- 12 a^{5} b^{4} c^{2}$ .

$\frac{4 a^{5} b^{4} (8 a^{3} b^{2}) + 4 a^{5} b^{4} (- 3 c^{2})}{4 a^{3} b^{3}}$

Factor $4 a^{5} b^{4}$ out of $4 a^{5} b^{4} (8 a^{3} b^{2}) + 4 a^{5} b^{4} (- 3 c^{2})$ .

$\frac{4 a^{5} b^{4} (8 a^{3} b^{2} - 3 c^{2})}{4 a^{3} b^{3}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 a^{5} b^{4} (8 a^{3} b^{2} - 3 c^{2})}{4 a^{3} b^{3}}$

Rewrite the expression.

$\frac{a^{5} b^{4} (8 a^{3} b^{2} - 3 c^{2})}{a^{3} b^{3}}$

Cancel the common factor of $a^{5}$ and $a^{3}$ .

Factor $a^{3}$ out of $a^{5} b^{4} (8 a^{3} b^{2} - 3 c^{2})$ .

$\frac{a^{3} (a^{2} b^{4} (8 a^{3} b^{2} - 3 c^{2}))}{a^{3} b^{3}}$

Cancel the common factors.

Factor $a^{3}$ out of $a^{3} b^{3}$ .

$\frac{a^{3} (a^{2} b^{4} (8 a^{3} b^{2} - 3 c^{2}))}{a^{3} (b^{3})}$

Cancel the common factor.

$\frac{a^{3} (a^{2} b^{4} (8 a^{3} b^{2} - 3 c^{2}))}{a^{3} b^{3}}$

Rewrite the expression.

$\frac{a^{2} b^{4} (8 a^{3} b^{2} - 3 c^{2})}{b^{3}}$

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

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

$\frac{b^{3} (a^{2} b (8 a^{3} b^{2} - 3 c^{2}))}{b^{3}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{b^{3} (a^{2} b (8 a^{3} b^{2} - 3 c^{2}))}{b^{3} \cdot 1}$

Cancel the common factor.

$\frac{b^{3} (a^{2} b (8 a^{3} b^{2} - 3 c^{2}))}{b^{3} \cdot 1}$

Rewrite the expression.

$\frac{a^{2} b (8 a^{3} b^{2} - 3 c^{2})}{1}$

Divide $a^{2} b (8 a^{3} b^{2} - 3 c^{2})$ by $1$ .

$a^{2} b (8 a^{3} b^{2} - 3 c^{2})$

Apply the distributive property.

$a^{2} b (8 a^{3} b^{2}) + a^{2} b (- 3 c^{2})$

Reorder.

Rewrite using the commutative property of multiplication.

$8 a^{2} b (a^{3} b^{2}) + a^{2} b (- 3 c^{2})$

Rewrite using the commutative property of multiplication.

$8 a^{2} b (a^{3} b^{2}) - 3 a^{2} b c^{2}$

Simplify each term.

Multiply $a^{2}$ by $a^{3}$ by adding the exponents.

Move $a^{3}$ .

$8 (a^{3} a^{2}) b \cdot b^{2} - 3 a^{2} b c^{2}$

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

$8 a^{3 + 2} b \cdot b^{2} - 3 a^{2} b c^{2}$

Add $3$ and $2$ .

$8 a^{5} b \cdot b^{2} - 3 a^{2} b c^{2}$

Multiply $b$ by $b^{2}$ by adding the exponents.

Move $b^{2}$ .

$8 a^{5} (b^{2} b) - 3 a^{2} b c^{2}$

Multiply $b^{2}$ by $b$ .

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

$8 a^{5} (b^{2} b^{1}) - 3 a^{2} b c^{2}$

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

$8 a^{5} b^{2 + 1} - 3 a^{2} b c^{2}$

Add $2$ and $1$ .

$8 a^{5} b^{3} - 3 a^{2} b c^{2}$

Simplify (32a^8b^6-12a^5b^4c^2)/(4a^3b^3)

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