Expand using Pascal’s Triangle (1+2i)^3

Math
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 .
The expansion follows the rule . The values of the coefficients, from the triangle, are .
Substitute the actual values of and into the expression.
Simplify the expression.
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Simplify each term.
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Multiply by by adding the exponents.
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Multiply by .
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Raise to the power of .
Use the power rule to combine exponents.
Add and .
Simplify .
One to any power is one.
One to any power is one.
Multiply by .
Simplify.
Multiply by .
Evaluate the exponent.
Multiply by .
Apply the product rule to .
Raise to the power of .
Rewrite as .
Multiply by .
Multiply by .
Multiply by by adding the exponents.
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Multiply by .
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Raise to the power of .
Use the power rule to combine exponents.
Add and .
Simplify .
Apply the product rule to .
Raise to the power of .
Factor out .
Rewrite as .
Rewrite as .
Multiply by .
Simplify by adding terms.
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Subtract from .
Subtract from .
Expand using Pascal’s Triangle (1+2i)^3

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