Use the binomial expansion theorem to find each term. The binomial theorem states .

Expand the summation.

Simplify the exponents for each term of the expansion.

Multiply by .

Apply the product rule to .

Raise to the power of .

Apply the product rule to .

Rewrite using the commutative property of multiplication.

Anything raised to is .

Multiply by .

Anything raised to is .

Multiply by .

Simplify.

Multiply by .

Simplify.

Rewrite using the commutative property of multiplication.

Multiply by .

Multiply by .

Apply the product rule to .

Anything raised to is .

Multiply by .

Anything raised to is .

Multiply by .

Apply the product rule to .

Raise to the power of .

Expand using the Binomial Theorem (4x+5y)^2