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 .

Apply the product rule to .

Anything raised to is .

Anything raised to is .

Divide by .

Multiply by .

Simplify.

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Apply the product rule to .

One to any power is one.

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Apply the product rule to .

One to any power is one.

Cancel the common factor of .

Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Combine and .

Simplify.

Apply the product rule to .

One to any power is one.

Cancel the common factor of .

Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Combine and .

Multiply by .

Anything raised to is .

Multiply by .

Apply the product rule to .

One to any power is one.

Expand Using Pascal’s Triangle (p+1/p)^5