Basic Math Examples

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

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

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Step 2.1

Multiply the exponents in ${(a^{2})}^{3}$ .

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Step 2.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 2.1.2

Multiply $2$ by $3$ .

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

Step 2.2

Rewrite using the commutative property of multiplication.

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

Step 2.3

Multiply $3$ by $- 1$ .

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

Step 2.4

Multiply the exponents in ${(a^{2})}^{2}$ .

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Step 2.4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$a^{6} - 3 a^{2 \cdot 2} b^{2} + 3 a^{2} {(- b^{2})}^{2} + {(- b^{2})}^{3} + {(b^{2} - c^{2})}^{3} + {(c^{2} - a^{2})}^{3}$

Step 2.4.2

Multiply $2$ by $2$ .

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

Step 2.5

Apply the product rule to $- b^{2}$ .

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

Step 2.6

Rewrite using the commutative property of multiplication.

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

Step 2.7

Raise $- 1$ to the power of $2$ .

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

Step 2.8

Multiply $3$ by $1$ .

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

Step 2.9

Multiply the exponents in ${(b^{2})}^{2}$ .

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Step 2.9.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 2.9.2

Multiply $2$ by $2$ .

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

Step 2.10

Apply the product rule to $- b^{2}$ .

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

Step 2.11

Raise $- 1$ to the power of $3$ .

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

Step 2.12

Multiply the exponents in ${(b^{2})}^{3}$ .

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Step 2.12.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 2.12.2

Multiply $2$ by $3$ .

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

Step 3

Use the Binomial Theorem.

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

Step 4

Simplify each term.

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Step 4.1

Multiply the exponents in ${(b^{2})}^{3}$ .

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Step 4.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 4.1.2

Multiply $2$ by $3$ .

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

Step 4.2

Rewrite using the commutative property of multiplication.

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

Step 4.3

Multiply $3$ by $- 1$ .

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

Step 4.4

Multiply the exponents in ${(b^{2})}^{2}$ .

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Step 4.4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 4.4.2

Multiply $2$ by $2$ .

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

Step 4.5

Apply the product rule to $- c^{2}$ .

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

Step 4.6

Rewrite using the commutative property of multiplication.

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

Step 4.7

Raise $- 1$ to the power of $2$ .

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

Step 4.8

Multiply $3$ by $1$ .

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

Step 4.9

Multiply the exponents in ${(c^{2})}^{2}$ .

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Step 4.9.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 4.9.2

Multiply $2$ by $2$ .

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

Step 4.10

Apply the product rule to $- c^{2}$ .

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

Step 4.11

Raise $- 1$ to the power of $3$ .

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

Step 4.12

Multiply the exponents in ${(c^{2})}^{3}$ .

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Step 4.12.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 4.12.2

Multiply $2$ by $3$ .

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

Step 5

Use the Binomial Theorem.

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

Step 6

Simplify each term.

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Step 6.1

Multiply the exponents in ${(c^{2})}^{3}$ .

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Step 6.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 6.1.2

Multiply $2$ by $3$ .

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

Step 6.2

Rewrite using the commutative property of multiplication.

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

Step 6.3

Multiply $3$ by $- 1$ .

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

Step 6.4

Multiply the exponents in ${(c^{2})}^{2}$ .

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Step 6.4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 6.4.2

Multiply $2$ by $2$ .

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

Step 6.5

Apply the product rule to $- a^{2}$ .

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

Step 6.6

Rewrite using the commutative property of multiplication.

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

Step 6.7

Raise $- 1$ to the power of $2$ .

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

Step 6.8

Multiply $3$ by $1$ .

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

Step 6.9

Multiply the exponents in ${(a^{2})}^{2}$ .

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Step 6.9.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 6.9.2

Multiply $2$ by $2$ .

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

Step 6.10

Apply the product rule to $- a^{2}$ .

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

Step 6.11

Raise $- 1$ to the power of $3$ .

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

Step 6.12

Multiply the exponents in ${(a^{2})}^{3}$ .

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Step 6.12.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$a^{6} - 3 a^{4} b^{2} + 3 a^{2} b^{4} - b^{6} + b^{6} - 3 b^{4} c^{2} + 3 b^{2} c^{4} - c^{6} + c^{6} - 3 c^{4} a^{2} + 3 c^{2} a^{4} - a^{2 \cdot 3}$

Step 6.12.2

Multiply $2$ by $3$ .

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

Step 7

Subtract $a^{6}$ from $a^{6}$ .

$- 3 a^{4} b^{2} + 3 a^{2} b^{4} - b^{6} + b^{6} - 3 b^{4} c^{2} + 3 b^{2} c^{4} - c^{6} + c^{6} - 3 c^{4} a^{2} + 3 c^{2} a^{4} + 0$

Step 8

Add $- 3 a^{4} b^{2} + 3 a^{2} b^{4} - b^{6} + b^{6} - 3 b^{4} c^{2} + 3 b^{2} c^{4} - c^{6} + c^{6} - 3 c^{4} a^{2} + 3 c^{2} a^{4}$ and $0$ .

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

Step 9

Add $- b^{6}$ and $b^{6}$ .

$- 3 a^{4} b^{2} + 3 a^{2} b^{4} + 0 - 3 b^{4} c^{2} + 3 b^{2} c^{4} - c^{6} + c^{6} - 3 c^{4} a^{2} + 3 c^{2} a^{4}$

Step 10

Add $- 3 a^{4} b^{2}$ and $0$ .

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

Step 11

Add $- c^{6}$ and $c^{6}$ .

$- 3 a^{4} b^{2} + 3 a^{2} b^{4} - 3 b^{4} c^{2} + 3 b^{2} c^{4} + 0 - 3 c^{4} a^{2} + 3 c^{2} a^{4}$

Step 12

Add $- 3 a^{4} b^{2}$ and $0$ .

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

Step 13

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

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Step 13.1

Factor $3$ out of $- 3 a^{4} b^{2}$ .

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

Step 13.2

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

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

Step 13.3

Factor $3$ out of $- 3 b^{4} c^{2}$ .

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

Step 13.4

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

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

Step 13.5

Factor $3$ out of $- 3 c^{4} a^{2}$ .

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

Step 13.6

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

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

Step 13.7

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

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

Step 13.8

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

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

Step 13.9

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

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

Step 13.10

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

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

Step 13.11

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

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