Finite Math Examples

Expand Using Pascal's Triangle (1+2i)^3
Step 1
Pascal's Triangle can be displayed as such:
The triangle can be used to calculate the coefficients of the expansion of by taking the exponent and adding . The coefficients will correspond with line of the triangle. For , so the coefficients of the expansion will correspond with line .
Step 2
The expansion follows the rule . The values of the coefficients, from the triangle, are .
Step 3
Substitute the actual values of and into the expression.
Step 4
Simplify the expression.
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Step 4.1
Simplify each term.
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Step 4.1.1
Multiply by by adding the exponents.
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Step 4.1.1.1
Multiply by .
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Step 4.1.1.1.1
Raise to the power of .
Step 4.1.1.1.2
Use the power rule to combine exponents.
Step 4.1.1.2
Add and .
Step 4.1.2
Simplify .
Step 4.1.3
One to any power is one.
Step 4.1.4
One to any power is one.
Step 4.1.5
Multiply by .
Step 4.1.6
Simplify.
Step 4.1.7
Multiply by .
Step 4.1.8
Evaluate the exponent.
Step 4.1.9
Multiply by .
Step 4.1.10
Apply the product rule to .
Step 4.1.11
Raise to the power of .
Step 4.1.12
Rewrite as .
Step 4.1.13
Multiply .
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Step 4.1.13.1
Multiply by .
Step 4.1.13.2
Multiply by .
Step 4.1.14
Multiply by by adding the exponents.
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Step 4.1.14.1
Multiply by .
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Step 4.1.14.1.1
Raise to the power of .
Step 4.1.14.1.2
Use the power rule to combine exponents.
Step 4.1.14.2
Add and .
Step 4.1.15
Simplify .
Step 4.1.16
Apply the product rule to .
Step 4.1.17
Raise to the power of .
Step 4.1.18
Factor out .
Step 4.1.19
Rewrite as .
Step 4.1.20
Rewrite as .
Step 4.1.21
Multiply by .
Step 4.2
Simplify by adding terms.
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Step 4.2.1
Subtract from .
Step 4.2.2
Subtract from .