Pre-Algebra Examples

Write as an Equation f(x)=(2x+3)^4*(x-3)^5
Step 1
Rewrite the function as an equation.
Step 2
Simplify .
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Step 2.1
Use the Binomial Theorem.
Step 2.2
Simplify each term.
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Step 2.2.1
Apply the product rule to .
Step 2.2.2
Raise to the power of .
Step 2.2.3
Apply the product rule to .
Step 2.2.4
Raise to the power of .
Step 2.2.5
Multiply by .
Step 2.2.6
Multiply by .
Step 2.2.7
Apply the product rule to .
Step 2.2.8
Raise to the power of .
Step 2.2.9
Multiply by .
Step 2.2.10
Raise to the power of .
Step 2.2.11
Multiply by .
Step 2.2.12
Multiply by .
Step 2.2.13
Raise to the power of .
Step 2.2.14
Multiply by .
Step 2.2.15
Raise to the power of .
Step 2.3
Use the Binomial Theorem.
Step 2.4
Simplify each term.
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Step 2.4.1
Multiply by .
Step 2.4.2
Raise to the power of .
Step 2.4.3
Multiply by .
Step 2.4.4
Raise to the power of .
Step 2.4.5
Multiply by .
Step 2.4.6
Raise to the power of .
Step 2.4.7
Multiply by .
Step 2.4.8
Raise to the power of .
Step 2.5
Expand by multiplying each term in the first expression by each term in the second expression.
Step 2.6
Simplify terms.
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Step 2.6.1
Simplify each term.
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Step 2.6.1.1
Multiply by by adding the exponents.
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Step 2.6.1.1.1
Move .
Step 2.6.1.1.2
Use the power rule to combine exponents.
Step 2.6.1.1.3
Add and .
Step 2.6.1.2
Rewrite using the commutative property of multiplication.
Step 2.6.1.3
Multiply by by adding the exponents.
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Step 2.6.1.3.1
Move .
Step 2.6.1.3.2
Use the power rule to combine exponents.
Step 2.6.1.3.3
Add and .
Step 2.6.1.4
Multiply by .
Step 2.6.1.5
Rewrite using the commutative property of multiplication.
Step 2.6.1.6
Multiply by by adding the exponents.
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Step 2.6.1.6.1
Move .
Step 2.6.1.6.2
Use the power rule to combine exponents.
Step 2.6.1.6.3
Add and .
Step 2.6.1.7
Multiply by .
Step 2.6.1.8
Rewrite using the commutative property of multiplication.
Step 2.6.1.9
Multiply by by adding the exponents.
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Step 2.6.1.9.1
Move .
Step 2.6.1.9.2
Use the power rule to combine exponents.
Step 2.6.1.9.3
Add and .
Step 2.6.1.10
Multiply by .
Step 2.6.1.11
Rewrite using the commutative property of multiplication.
Step 2.6.1.12
Multiply by by adding the exponents.
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Step 2.6.1.12.1
Move .
Step 2.6.1.12.2
Multiply by .
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Step 2.6.1.12.2.1
Raise to the power of .
Step 2.6.1.12.2.2
Use the power rule to combine exponents.
Step 2.6.1.12.3
Add and .
Step 2.6.1.13
Multiply by .
Step 2.6.1.14
Multiply by .
Step 2.6.1.15
Multiply by by adding the exponents.
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Step 2.6.1.15.1
Move .
Step 2.6.1.15.2
Use the power rule to combine exponents.
Step 2.6.1.15.3
Add and .
Step 2.6.1.16
Rewrite using the commutative property of multiplication.
Step 2.6.1.17
Multiply by by adding the exponents.
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Step 2.6.1.17.1
Move .
Step 2.6.1.17.2
Use the power rule to combine exponents.
Step 2.6.1.17.3
Add and .
Step 2.6.1.18
Multiply by .
Step 2.6.1.19
Rewrite using the commutative property of multiplication.
Step 2.6.1.20
Multiply by by adding the exponents.
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Step 2.6.1.20.1
Move .
Step 2.6.1.20.2
Use the power rule to combine exponents.
Step 2.6.1.20.3
Add and .
Step 2.6.1.21
Multiply by .
Step 2.6.1.22
Rewrite using the commutative property of multiplication.
Step 2.6.1.23
Multiply by by adding the exponents.
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Step 2.6.1.23.1
Move .
Step 2.6.1.23.2
Use the power rule to combine exponents.
Step 2.6.1.23.3
Add and .
Step 2.6.1.24
Multiply by .
Step 2.6.1.25
Rewrite using the commutative property of multiplication.
Step 2.6.1.26
Multiply by by adding the exponents.
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Step 2.6.1.26.1
Move .
Step 2.6.1.26.2
Multiply by .
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Step 2.6.1.26.2.1
Raise to the power of .
Step 2.6.1.26.2.2
Use the power rule to combine exponents.
Step 2.6.1.26.3
Add and .
Step 2.6.1.27
Multiply by .
Step 2.6.1.28
Multiply by .
Step 2.6.1.29
Multiply by by adding the exponents.
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Step 2.6.1.29.1
Move .
Step 2.6.1.29.2
Use the power rule to combine exponents.
Step 2.6.1.29.3
Add and .
Step 2.6.1.30
Rewrite using the commutative property of multiplication.
Step 2.6.1.31
Multiply by by adding the exponents.
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Step 2.6.1.31.1
Move .
Step 2.6.1.31.2
Use the power rule to combine exponents.
Step 2.6.1.31.3
Add and .
Step 2.6.1.32
Multiply by .
Step 2.6.1.33
Rewrite using the commutative property of multiplication.
Step 2.6.1.34
Multiply by by adding the exponents.
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Step 2.6.1.34.1
Move .
Step 2.6.1.34.2
Use the power rule to combine exponents.
Step 2.6.1.34.3
Add and .
Step 2.6.1.35
Multiply by .
Step 2.6.1.36
Rewrite using the commutative property of multiplication.
Step 2.6.1.37
Multiply by by adding the exponents.
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Step 2.6.1.37.1
Move .
Step 2.6.1.37.2
Use the power rule to combine exponents.
Step 2.6.1.37.3
Add and .
Step 2.6.1.38
Multiply by .
Step 2.6.1.39
Rewrite using the commutative property of multiplication.
Step 2.6.1.40
Multiply by by adding the exponents.
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Step 2.6.1.40.1
Move .
Step 2.6.1.40.2
Multiply by .
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Step 2.6.1.40.2.1
Raise to the power of .
Step 2.6.1.40.2.2
Use the power rule to combine exponents.
Step 2.6.1.40.3
Add and .
Step 2.6.1.41
Multiply by .
Step 2.6.1.42
Multiply by .
Step 2.6.1.43
Multiply by by adding the exponents.
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Step 2.6.1.43.1
Move .
Step 2.6.1.43.2
Multiply by .
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Step 2.6.1.43.2.1
Raise to the power of .
Step 2.6.1.43.2.2
Use the power rule to combine exponents.
Step 2.6.1.43.3
Add and .
Step 2.6.1.44
Rewrite using the commutative property of multiplication.
Step 2.6.1.45
Multiply by by adding the exponents.
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Step 2.6.1.45.1
Move .
Step 2.6.1.45.2
Multiply by .
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Step 2.6.1.45.2.1
Raise to the power of .
Step 2.6.1.45.2.2
Use the power rule to combine exponents.
Step 2.6.1.45.3
Add and .
Step 2.6.1.46
Multiply by .
Step 2.6.1.47
Rewrite using the commutative property of multiplication.
Step 2.6.1.48
Multiply by by adding the exponents.
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Step 2.6.1.48.1
Move .
Step 2.6.1.48.2
Multiply by .
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Step 2.6.1.48.2.1
Raise to the power of .
Step 2.6.1.48.2.2
Use the power rule to combine exponents.
Step 2.6.1.48.3
Add and .
Step 2.6.1.49
Multiply by .
Step 2.6.1.50
Rewrite using the commutative property of multiplication.
Step 2.6.1.51
Multiply by by adding the exponents.
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Step 2.6.1.51.1
Move .
Step 2.6.1.51.2
Multiply by .
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Step 2.6.1.51.2.1
Raise to the power of .
Step 2.6.1.51.2.2
Use the power rule to combine exponents.
Step 2.6.1.51.3
Add and .
Step 2.6.1.52
Multiply by .
Step 2.6.1.53
Rewrite using the commutative property of multiplication.
Step 2.6.1.54
Multiply by by adding the exponents.
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Step 2.6.1.54.1
Move .
Step 2.6.1.54.2
Multiply by .
Step 2.6.1.55
Multiply by .
Step 2.6.1.56
Multiply by .
Step 2.6.1.57
Multiply by .
Step 2.6.1.58
Multiply by .
Step 2.6.1.59
Multiply by .
Step 2.6.1.60
Multiply by .
Step 2.6.1.61
Multiply by .
Step 2.6.2
Simplify by adding terms.
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Step 2.6.2.1
Combine the opposite terms in .
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Step 2.6.2.1.1
Subtract from .
Step 2.6.2.1.2
Add and .
Step 2.6.2.2
Add and .
Step 2.6.2.3
Add and .
Step 2.6.2.4
Subtract from .
Step 2.6.2.5
Add and .
Step 2.6.2.6
Subtract from .
Step 2.6.2.7
Combine the opposite terms in .
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Step 2.6.2.7.1
Add and .
Step 2.6.2.7.2
Add and .
Step 2.6.2.8
Add and .
Step 2.6.2.9
Subtract from .
Step 2.6.2.10
Add and .
Step 2.6.2.11
Subtract from .
Step 2.6.2.12
Add and .
Step 2.6.2.13
Subtract from .
Step 2.6.2.14
Add and .
Step 2.6.2.15
Add and .
Step 2.6.2.16
Add and .
Step 2.6.2.17
Subtract from .
Step 2.6.2.18
Add and .
Step 2.6.2.19
Reorder.
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Step 2.6.2.19.1
Move .
Step 2.6.2.19.2
Move .
Step 2.6.2.19.3
Move .