Finite Math Examples

Simplify 15x^3(x+y)^2-30x^2(x+y)-45x(x+y)^4
Step 1
Simplify each term.
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Step 1.1
Rewrite as .
Step 1.2
Expand using the FOIL Method.
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Step 1.2.1
Apply the distributive property.
Step 1.2.2
Apply the distributive property.
Step 1.2.3
Apply the distributive property.
Step 1.3
Simplify and combine like terms.
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Step 1.3.1
Simplify each term.
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Step 1.3.1.1
Multiply by .
Step 1.3.1.2
Multiply by .
Step 1.3.2
Add and .
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Step 1.3.2.1
Reorder and .
Step 1.3.2.2
Add and .
Step 1.4
Apply the distributive property.
Step 1.5
Simplify.
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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
Use the power rule to combine exponents.
Step 1.5.1.3
Add and .
Step 1.5.2
Multiply by by adding the exponents.
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Step 1.5.2.1
Move .
Step 1.5.2.2
Multiply by .
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Step 1.5.2.2.1
Raise to the power of .
Step 1.5.2.2.2
Use the power rule to combine exponents.
Step 1.5.2.3
Add and .
Step 1.6
Simplify each term.
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Step 1.6.1
Rewrite using the commutative property of multiplication.
Step 1.6.2
Multiply by .
Step 1.7
Apply the distributive property.
Step 1.8
Multiply by by adding the exponents.
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Step 1.8.1
Move .
Step 1.8.2
Multiply by .
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Step 1.8.2.1
Raise to the power of .
Step 1.8.2.2
Use the power rule to combine exponents.
Step 1.8.3
Add and .
Step 1.9
Use the Binomial Theorem.
Step 1.10
Apply the distributive property.
Step 1.11
Simplify.
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Step 1.11.1
Multiply by by adding the exponents.
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Step 1.11.1.1
Move .
Step 1.11.1.2
Multiply by .
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Step 1.11.1.2.1
Raise to the power of .
Step 1.11.1.2.2
Use the power rule to combine exponents.
Step 1.11.1.3
Add and .
Step 1.11.2
Multiply by by adding the exponents.
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Step 1.11.2.1
Move .
Step 1.11.2.2
Multiply by .
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Step 1.11.2.2.1
Raise to the power of .
Step 1.11.2.2.2
Use the power rule to combine exponents.
Step 1.11.2.3
Add and .
Step 1.11.3
Multiply by by adding the exponents.
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Step 1.11.3.1
Move .
Step 1.11.3.2
Multiply by .
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Step 1.11.3.2.1
Raise to the power of .
Step 1.11.3.2.2
Use the power rule to combine exponents.
Step 1.11.3.3
Add and .
Step 1.11.4
Multiply by by adding the exponents.
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Step 1.11.4.1
Move .
Step 1.11.4.2
Multiply by .
Step 1.12
Simplify each term.
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Step 1.12.1
Rewrite using the commutative property of multiplication.
Step 1.12.2
Multiply by .
Step 1.12.3
Rewrite using the commutative property of multiplication.
Step 1.12.4
Multiply by .
Step 1.12.5
Rewrite using the commutative property of multiplication.
Step 1.12.6
Multiply by .
Step 2
Simplify by adding terms.
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Step 2.1
Subtract from .
Step 2.2
Subtract from .
Step 2.3
Subtract from .