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.

Multiply by by adding the exponents.

Move .

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Simplify .

Evaluate the exponent.

Multiply by .

One to any power is one.

Multiply by .

One to any power is one.

Multiply by .

One to any power is one.

Multiply by .

One to any power is one.

Multiply by .

One to any power is one.

Multiply by .

One to any power is one.

Multiply by .

Simplify.

One to any power is one.

Multiply by .

Multiply by by adding the exponents.

Move .

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Simplify .

One to any power is one.

Expand Using Pascal’s Triangle (x+1)^9