Question

If (x + y)^4 = x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4, expand (r + 2)^4.

r^4 + 8r^3 + 24r^2 + 32r + 16
r^4 + 8r^3 + 24r^2 + 8r + 16
r^4 + 2r^3 + 4r^2 + 8r + 16
r^4 + 8r^3 + 12r^2 + 8r + 16
none of the answer choices

Answer 1

Use x = r and y = 2 in the binomial expansion:

(r + 2)^4 = r^4 + 4r^3(2) + 6r^2(2^2) + 4r(2^3) + 2^4
= r^4 + 8r^3 + 24r^2 + 32r + 16.

So the correct choice is the first one: r^4 + 8r^3 + 24r^2 + 32r + 16.