Basic Math Examples

Simplify ((a-b)^2)/((b-c)*(c-a))+((b-c)^2)/((c-a)*(a-b))+((c-a)^2)/((a-b)*(b-c))
Step 1
Multiply by .
Step 2
To write as a fraction with a common denominator, multiply by .
Step 3
To write as a fraction with a common denominator, multiply by .
Step 4
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 4.1
Multiply by .
Step 4.2
Multiply by .
Step 4.3
Reorder the factors of .
Step 4.4
Reorder the factors of .
Step 5
Combine the numerators over the common denominator.
Step 6
Simplify each term.
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Step 6.1
Simplify the numerator.
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Step 6.1.1
Multiply by by adding the exponents.
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Step 6.1.1.1
Multiply by .
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Step 6.1.1.1.1
Raise to the power of .
Step 6.1.1.1.2
Use the power rule to combine exponents.
Step 6.1.1.2
Add and .
Step 6.1.2
Multiply by by adding the exponents.
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Step 6.1.2.1
Multiply by .
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Step 6.1.2.1.1
Raise to the power of .
Step 6.1.2.1.2
Use the power rule to combine exponents.
Step 6.1.2.2
Add and .
Step 6.1.3
Since both terms are perfect cubes, factor using the sum of cubes formula, where and .
Step 6.1.4
Simplify.
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Step 6.1.4.1
Add and .
Step 6.1.4.2
Add and .
Step 6.1.4.3
Rewrite as .
Step 6.1.4.4
Expand using the FOIL Method.
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Step 6.1.4.4.1
Apply the distributive property.
Step 6.1.4.4.2
Apply the distributive property.
Step 6.1.4.4.3
Apply the distributive property.
Step 6.1.4.5
Simplify and combine like terms.
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Step 6.1.4.5.1
Simplify each term.
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Step 6.1.4.5.1.1
Multiply by .
Step 6.1.4.5.1.2
Rewrite using the commutative property of multiplication.
Step 6.1.4.5.1.3
Rewrite using the commutative property of multiplication.
Step 6.1.4.5.1.4
Multiply by by adding the exponents.
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Step 6.1.4.5.1.4.1
Move .
Step 6.1.4.5.1.4.2
Multiply by .
Step 6.1.4.5.1.5
Multiply by .
Step 6.1.4.5.1.6
Multiply by .
Step 6.1.4.5.2
Subtract from .
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Step 6.1.4.5.2.1
Move .
Step 6.1.4.5.2.2
Subtract from .
Step 6.1.4.6
Apply the distributive property.
Step 6.1.4.7
Multiply .
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Step 6.1.4.7.1
Multiply by .
Step 6.1.4.7.2
Multiply by .
Step 6.1.4.8
Expand using the FOIL Method.
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Step 6.1.4.8.1
Apply the distributive property.
Step 6.1.4.8.2
Apply the distributive property.
Step 6.1.4.8.3
Apply the distributive property.
Step 6.1.4.9
Simplify each term.
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Step 6.1.4.9.1
Rewrite using the commutative property of multiplication.
Step 6.1.4.9.2
Multiply by .
Step 6.1.4.9.3
Multiply by .
Step 6.1.4.9.4
Multiply by .
Step 6.1.4.9.5
Rewrite using the commutative property of multiplication.
Step 6.1.4.10
Rewrite as .
Step 6.1.4.11
Expand using the FOIL Method.
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Step 6.1.4.11.1
Apply the distributive property.
Step 6.1.4.11.2
Apply the distributive property.
Step 6.1.4.11.3
Apply the distributive property.
Step 6.1.4.12
Simplify and combine like terms.
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Step 6.1.4.12.1
Simplify each term.
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Step 6.1.4.12.1.1
Multiply by .
Step 6.1.4.12.1.2
Rewrite using the commutative property of multiplication.
Step 6.1.4.12.1.3
Rewrite using the commutative property of multiplication.
Step 6.1.4.12.1.4
Multiply by by adding the exponents.
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Step 6.1.4.12.1.4.1
Move .
Step 6.1.4.12.1.4.2
Multiply by .
Step 6.1.4.12.1.5
Multiply by .
Step 6.1.4.12.1.6
Multiply by .
Step 6.1.4.12.2
Subtract from .
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Step 6.1.4.12.2.1
Move .
Step 6.1.4.12.2.2
Subtract from .
Step 6.1.4.13
Subtract from .
Step 6.1.4.14
Add and .
Step 6.1.4.15
Add and .
Step 6.1.4.16
Subtract from .
Step 6.2
Cancel the common factor of and .
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Step 6.2.1
Factor out of .
Step 6.2.2
Factor out of .
Step 6.2.3
Factor out of .
Step 6.2.4
Reorder terms.
Step 6.2.5
Cancel the common factor.
Step 6.2.6
Rewrite the expression.
Step 6.3
Move the negative in front of the fraction.
Step 7
Combine the numerators over the common denominator.
Step 8
Simplify each term.
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Step 8.1
Apply the distributive property.
Step 8.2
Simplify.
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Step 8.2.1
Multiply by .
Step 8.2.2
Multiply by .
Step 8.2.3
Multiply by .
Step 8.3
Remove parentheses.
Step 8.4
Rewrite as .
Step 8.5
Expand using the FOIL Method.
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Step 8.5.1
Apply the distributive property.
Step 8.5.2
Apply the distributive property.
Step 8.5.3
Apply the distributive property.
Step 8.6
Simplify and combine like terms.
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Step 8.6.1
Simplify each term.
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Step 8.6.1.1
Multiply by .
Step 8.6.1.2
Rewrite using the commutative property of multiplication.
Step 8.6.1.3
Rewrite using the commutative property of multiplication.
Step 8.6.1.4
Multiply by by adding the exponents.
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Step 8.6.1.4.1
Move .
Step 8.6.1.4.2
Multiply by .
Step 8.6.1.5
Multiply by .
Step 8.6.1.6
Multiply by .
Step 8.6.2
Subtract from .
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Step 8.6.2.1
Move .
Step 8.6.2.2
Subtract from .
Step 9
Simplify terms.
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Step 9.1
Combine the opposite terms in .
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Step 9.1.1
Add and .
Step 9.1.2
Add and .
Step 9.1.3
Add and .
Step 9.1.4
Add and .
Step 9.2
Subtract from .
Step 9.3
Factor out of .
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Step 9.3.1
Factor out of .
Step 9.3.2
Factor out of .
Step 9.3.3
Factor out of .
Step 9.3.4
Factor out of .
Step 9.3.5
Factor out of .
Step 9.3.6
Factor out of .
Step 9.3.7
Factor out of .
Step 9.4
Factor out of .
Step 9.5
Factor out of .
Step 9.6
Factor out of .
Step 9.7
Factor out of .
Step 9.8
Factor out of .
Step 9.9
Factor out of .
Step 9.10
Factor out of .
Step 9.11
Simplify the expression.
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Step 9.11.1
Rewrite as .
Step 9.11.2
Move the negative in front of the fraction.