Trigonometry Examples

Simplify 6x(3x+1)^3-(3x+1)^4
Step 1
Simplify each term.
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Step 1.1
Use the Binomial Theorem.
Step 1.2
Simplify each term.
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Step 1.2.1
Apply the product rule to .
Step 1.2.2
Raise to the power of .
Step 1.2.3
Apply the product rule to .
Step 1.2.4
Multiply by by adding the exponents.
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Step 1.2.4.1
Move .
Step 1.2.4.2
Multiply by .
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Step 1.2.4.2.1
Raise to the power of .
Step 1.2.4.2.2
Use the power rule to combine exponents.
Step 1.2.4.3
Add and .
Step 1.2.5
Simplify .
Step 1.2.6
Raise to the power of .
Step 1.2.7
Multiply by .
Step 1.2.8
One to any power is one.
Step 1.2.9
Multiply by .
Step 1.2.10
One to any power is one.
Step 1.3
Apply the distributive property.
Step 1.4
Simplify.
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Step 1.4.1
Rewrite using the commutative property of multiplication.
Step 1.4.2
Rewrite using the commutative property of multiplication.
Step 1.4.3
Rewrite using the commutative property of multiplication.
Step 1.4.4
Multiply by .
Step 1.5
Simplify each term.
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Step 1.5.1
Multiply by by adding the exponents.
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Step 1.5.1.1
Move .
Step 1.5.1.2
Multiply by .
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Step 1.5.1.2.1
Raise to the power of .
Step 1.5.1.2.2
Use the power rule to combine exponents.
Step 1.5.1.3
Add and .
Step 1.5.2
Multiply by .
Step 1.5.3
Multiply by by adding the exponents.
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Step 1.5.3.1
Move .
Step 1.5.3.2
Multiply by .
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Step 1.5.3.2.1
Raise to the power of .
Step 1.5.3.2.2
Use the power rule to combine exponents.
Step 1.5.3.3
Add and .
Step 1.5.4
Multiply by .
Step 1.5.5
Multiply by by adding the exponents.
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Step 1.5.5.1
Move .
Step 1.5.5.2
Multiply by .
Step 1.5.6
Multiply by .
Step 1.6
Use the Binomial Theorem.
Step 1.7
Simplify each term.
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Step 1.7.1
Apply the product rule to .
Step 1.7.2
Raise to the power of .
Step 1.7.3
Apply the product rule to .
Step 1.7.4
Raise to the power of .
Step 1.7.5
Multiply by .
Step 1.7.6
Multiply by .
Step 1.7.7
Apply the product rule to .
Step 1.7.8
Raise to the power of .
Step 1.7.9
Multiply by .
Step 1.7.10
One to any power is one.
Step 1.7.11
Multiply by .
Step 1.7.12
Multiply by .
Step 1.7.13
One to any power is one.
Step 1.7.14
Multiply by .
Step 1.7.15
One to any power is one.
Step 1.8
Apply the distributive property.
Step 1.9
Simplify.
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Step 1.9.1
Multiply by .
Step 1.9.2
Multiply by .
Step 1.9.3
Multiply by .
Step 1.9.4
Multiply by .
Step 1.9.5
Multiply by .
Step 2
Simplify by adding terms.
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Step 2.1
Combine the opposite terms in .
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Step 2.1.1
Subtract from .
Step 2.1.2
Add and .
Step 2.2
Subtract from .
Step 2.3
Subtract from .
Step 2.4
Subtract from .