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 .

Apply the product rule to .

Multiply by by adding the exponents.

Move .

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Simplify .

Rewrite using the commutative property of multiplication.

Raise to the power of .

Multiply by .

Apply the product rule to .

Raise to the power of .

Multiply by .

Apply the product rule to .

Rewrite using the commutative property of multiplication.

Raise to the power of .

Multiply by .

Simplify.

Multiply by .

Apply the product rule to .

Rewrite using the commutative property of multiplication.

Raise to the power of .

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 (4p+7q)^4