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 each term.

Multiply by by adding the exponents.

Multiply by .

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.

Multiply by .

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.

Subtract from .

Subtract from .

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