Calculus Examples

Multiply (x^4+9)^8(4x^3dx)
Step 1
Rewrite using the commutative property of multiplication.
Step 2
Multiply by by adding the exponents.
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Step 2.1
Move .
Step 2.2
Multiply by .
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Step 2.2.1
Raise to the power of .
Step 2.2.2
Use the power rule to combine exponents.
Step 2.3
Add and .
Step 3
Use the Binomial Theorem.
Step 4
Simplify terms.
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Step 4.1
Simplify each term.
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Step 4.1.1
Multiply the exponents in .
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Step 4.1.1.1
Apply the power rule and multiply exponents, .
Step 4.1.1.2
Multiply by .
Step 4.1.2
Multiply the exponents in .
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Step 4.1.2.1
Apply the power rule and multiply exponents, .
Step 4.1.2.2
Multiply by .
Step 4.1.3
Multiply by .
Step 4.1.4
Multiply the exponents in .
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Step 4.1.4.1
Apply the power rule and multiply exponents, .
Step 4.1.4.2
Multiply by .
Step 4.1.5
Raise to the power of .
Step 4.1.6
Multiply by .
Step 4.1.7
Multiply the exponents in .
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Step 4.1.7.1
Apply the power rule and multiply exponents, .
Step 4.1.7.2
Multiply by .
Step 4.1.8
Raise to the power of .
Step 4.1.9
Multiply by .
Step 4.1.10
Multiply the exponents in .
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Step 4.1.10.1
Apply the power rule and multiply exponents, .
Step 4.1.10.2
Multiply by .
Step 4.1.11
Raise to the power of .
Step 4.1.12
Multiply by .
Step 4.1.13
Multiply the exponents in .
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Step 4.1.13.1
Apply the power rule and multiply exponents, .
Step 4.1.13.2
Multiply by .
Step 4.1.14
Raise to the power of .
Step 4.1.15
Multiply by .
Step 4.1.16
Multiply the exponents in .
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Step 4.1.16.1
Apply the power rule and multiply exponents, .
Step 4.1.16.2
Multiply by .
Step 4.1.17
Raise to the power of .
Step 4.1.18
Multiply by .
Step 4.1.19
Raise to the power of .
Step 4.1.20
Multiply by .
Step 4.1.21
Raise to the power of .
Step 4.2
Apply the distributive property.
Step 5
Simplify.
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Step 5.1
Multiply by .
Step 5.2
Multiply by .
Step 5.3
Multiply by .
Step 5.4
Multiply by .
Step 5.5
Multiply by .
Step 5.6
Multiply by .
Step 5.7
Multiply by .
Step 5.8
Multiply by .
Step 6
Apply the distributive property.
Step 7
Simplify.
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Step 7.1
Multiply by by adding the exponents.
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Step 7.1.1
Move .
Step 7.1.2
Use the power rule to combine exponents.
Step 7.1.3
Add and .
Step 7.2
Multiply by by adding the exponents.
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Step 7.2.1
Move .
Step 7.2.2
Use the power rule to combine exponents.
Step 7.2.3
Add and .
Step 7.3
Multiply by by adding the exponents.
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Step 7.3.1
Move .
Step 7.3.2
Use the power rule to combine exponents.
Step 7.3.3
Add and .
Step 7.4
Multiply by by adding the exponents.
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Step 7.4.1
Move .
Step 7.4.2
Use the power rule to combine exponents.
Step 7.4.3
Add and .
Step 7.5
Multiply by by adding the exponents.
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Step 7.5.1
Move .
Step 7.5.2
Use the power rule to combine exponents.
Step 7.5.3
Add and .
Step 7.6
Multiply by by adding the exponents.
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Step 7.6.1
Move .
Step 7.6.2
Use the power rule to combine exponents.
Step 7.6.3
Add and .
Step 7.7
Multiply by by adding the exponents.
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Step 7.7.1
Move .
Step 7.7.2
Use the power rule to combine exponents.
Step 7.7.3
Add and .
Step 7.8
Multiply by by adding the exponents.
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Step 7.8.1
Move .
Step 7.8.2
Use the power rule to combine exponents.
Step 7.8.3
Add and .
Step 8
Apply the distributive property.