Algebra Examples

$\frac{16 a^{3} b^{2} c^{5} - 24 a^{5} b c^{4} + 44 a^{7} b^{6} c^{6}}{4 a^{2} b c^{3}}$

Step 1

Factor $4 a^{3} b c^{4}$ out of $16 a^{3} b^{2} c^{5} - 24 a^{5} b c^{4} + 44 a^{7} b^{6} c^{6}$ .

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Step 1.1

Factor $4 a^{3} b c^{4}$ out of $16 a^{3} b^{2} c^{5}$ .

$\frac{4 a^{3} b c^{4} (4 b c) - 24 a^{5} b c^{4} + 44 a^{7} b^{6} c^{6}}{4 a^{2} b c^{3}}$

Step 1.2

Factor $4 a^{3} b c^{4}$ out of $- 24 a^{5} b c^{4}$ .

$\frac{4 a^{3} b c^{4} (4 b c) + 4 a^{3} b c^{4} (- 6 a^{2}) + 44 a^{7} b^{6} c^{6}}{4 a^{2} b c^{3}}$

Step 1.3

Factor $4 a^{3} b c^{4}$ out of $44 a^{7} b^{6} c^{6}$ .

$\frac{4 a^{3} b c^{4} (4 b c) + 4 a^{3} b c^{4} (- 6 a^{2}) + 4 a^{3} b c^{4} (11 a^{4} b^{5} c^{2})}{4 a^{2} b c^{3}}$

Step 1.4

Factor $4 a^{3} b c^{4}$ out of $4 a^{3} b c^{4} (4 b c) + 4 a^{3} b c^{4} (- 6 a^{2})$ .

$\frac{4 a^{3} b c^{4} (4 b c - 6 a^{2}) + 4 a^{3} b c^{4} (11 a^{4} b^{5} c^{2})}{4 a^{2} b c^{3}}$

Step 1.5

Factor $4 a^{3} b c^{4}$ out of $4 a^{3} b c^{4} (4 b c - 6 a^{2}) + 4 a^{3} b c^{4} (11 a^{4} b^{5} c^{2})$ .

$\frac{4 a^{3} b c^{4} (4 b c - 6 a^{2} + 11 a^{4} b^{5} c^{2})}{4 a^{2} b c^{3}}$

Step 2

Cancel the common factor of $4$ .

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Step 2.1

Cancel the common factor.

$\frac{4 a^{3} b c^{4} (4 b c - 6 a^{2} + 11 a^{4} b^{5} c^{2})}{4 a^{2} b c^{3}}$

Step 2.2

Rewrite the expression.

$\frac{a^{3} b c^{4} (4 b c - 6 a^{2} + 11 a^{4} b^{5} c^{2})}{a^{2} b c^{3}}$

Step 3

Cancel the common factor of $a^{3}$ and $a^{2}$ .

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Step 3.1

Factor $a^{2}$ out of $a^{3} b c^{4} (4 b c - 6 a^{2} + 11 a^{4} b^{5} c^{2})$ .

$\frac{a^{2} (a b c^{4} (4 b c - 6 a^{2} + 11 a^{4} b^{5} c^{2}))}{a^{2} b c^{3}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $a^{2}$ out of $a^{2} b c^{3}$ .

$\frac{a^{2} (a b c^{4} (4 b c - 6 a^{2} + 11 a^{4} b^{5} c^{2}))}{a^{2} (b c^{3})}$

Step 3.2.2

Cancel the common factor.

$\frac{a^{2} (a b c^{4} (4 b c - 6 a^{2} + 11 a^{4} b^{5} c^{2}))}{a^{2} (b c^{3})}$

Step 3.2.3

Rewrite the expression.

$\frac{a b c^{4} (4 b c - 6 a^{2} + 11 a^{4} b^{5} c^{2})}{b c^{3}}$

Step 4

Cancel the common factor of $b$ .

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Step 4.1

Cancel the common factor.

$\frac{a b c^{4} (4 b c - 6 a^{2} + 11 a^{4} b^{5} c^{2})}{b c^{3}}$

Step 4.2

Rewrite the expression.

$\frac{a c^{4} (4 b c - 6 a^{2} + 11 a^{4} b^{5} c^{2})}{c^{3}}$

Step 5

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

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Step 5.1

Factor $c^{3}$ out of $a c^{4} (4 b c - 6 a^{2} + 11 a^{4} b^{5} c^{2})$ .

$\frac{c^{3} (a c (4 b c - 6 a^{2} + 11 a^{4} b^{5} c^{2}))}{c^{3}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Multiply by $1$ .

$\frac{c^{3} (a c (4 b c - 6 a^{2} + 11 a^{4} b^{5} c^{2}))}{c^{3} \cdot 1}$

Step 5.2.2

Cancel the common factor.

$\frac{c^{3} (a c (4 b c - 6 a^{2} + 11 a^{4} b^{5} c^{2}))}{c^{3} \cdot 1}$

Step 5.2.3

Rewrite the expression.

$\frac{a c (4 b c - 6 a^{2} + 11 a^{4} b^{5} c^{2})}{1}$

Step 5.2.4

Divide $a c (4 b c - 6 a^{2} + 11 a^{4} b^{5} c^{2})$ by $1$ .

$a c (4 b c - 6 a^{2} + 11 a^{4} b^{5} c^{2})$

Step 6

Apply the distributive property.

$a c (4 b c) + a c (- 6 a^{2}) + a c (11 a^{4} b^{5} c^{2})$

Step 7

Simplify.

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Step 7.1

Rewrite using the commutative property of multiplication.

$4 a c (b c) + a c (- 6 a^{2}) + a c (11 a^{4} b^{5} c^{2})$

Step 7.2

Rewrite using the commutative property of multiplication.

$4 a c (b c) - 6 a c a^{2} + a c (11 a^{4} b^{5} c^{2})$

Step 7.3

Rewrite using the commutative property of multiplication.

$4 a c (b c) - 6 a c a^{2} + 11 a c (a^{4} b^{5} c^{2})$

Step 8

Simplify each term.

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Step 8.1

Multiply $c$ by $c$ by adding the exponents.

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Step 8.1.1

Move $c$ .

$4 a (c \cdot c) b - 6 a c a^{2} + 11 a c (a^{4} b^{5} c^{2})$

Step 8.1.2

Multiply $c$ by $c$ .

$4 a c^{2} b - 6 a c a^{2} + 11 a c (a^{4} b^{5} c^{2})$

Step 8.2

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

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Step 8.2.1

Move $a^{2}$ .

$4 a c^{2} b - 6 (a^{2} a) c + 11 a c (a^{4} b^{5} c^{2})$

Step 8.2.2

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

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Step 8.2.2.1

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

$4 a c^{2} b - 6 (a^{2} a^{1}) c + 11 a c (a^{4} b^{5} c^{2})$

Step 8.2.2.2

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

$4 a c^{2} b - 6 a^{2 + 1} c + 11 a c (a^{4} b^{5} c^{2})$

Step 8.2.3

Add $2$ and $1$ .

$4 a c^{2} b - 6 a^{3} c + 11 a c (a^{4} b^{5} c^{2})$

Step 8.3

Multiply $a$ by $a^{4}$ by adding the exponents.

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Step 8.3.1

Move $a^{4}$ .

$4 a c^{2} b - 6 a^{3} c + 11 (a^{4} a) c (b^{5} c^{2})$

Step 8.3.2

Multiply $a^{4}$ by $a$ .

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Step 8.3.2.1

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

$4 a c^{2} b - 6 a^{3} c + 11 (a^{4} a^{1}) c (b^{5} c^{2})$

Step 8.3.2.2

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

$4 a c^{2} b - 6 a^{3} c + 11 a^{4 + 1} c (b^{5} c^{2})$

Step 8.3.3

Add $4$ and $1$ .

$4 a c^{2} b - 6 a^{3} c + 11 a^{5} c (b^{5} c^{2})$

Step 8.4

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

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Step 8.4.1

Move $c^{2}$ .

$4 a c^{2} b - 6 a^{3} c + 11 a^{5} (c^{2} c) b^{5}$

Step 8.4.2

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

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Step 8.4.2.1

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

$4 a c^{2} b - 6 a^{3} c + 11 a^{5} (c^{2} c^{1}) b^{5}$

Step 8.4.2.2

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

$4 a c^{2} b - 6 a^{3} c + 11 a^{5} c^{2 + 1} b^{5}$

Step 8.4.3

Add $2$ and $1$ .

$4 a c^{2} b - 6 a^{3} c + 11 a^{5} c^{3} b^{5}$