Expand using the binomial theorem.
-$$( 4 x + y ) ^ { 3 }$$
A) $64 x ^ { 3 } + 48 x ^ { 2 } + 12 y ^ { 2 } + y ^ { 3 }$
B) $64 x ^ { 3 } + 32 x ^ { 2 } y + 8 x y ^ { 2 } + y ^ { 3 }$
C) $64 x ^ { 3 } + 48 x ^ { 2 } y + 12 x y ^ { 2 } + y ^ { 3 }$
D) $64 x ^ { 3 } + 32 x ^ { 2 } + 8 y ^ { 2 } + y ^ { 3 }$

Question

Quizplus · Accepted Answer

Using the binomial theorem, we can expand $$(4x+y)^3 = \binom{3}{0}(4x)^3y^0 + \binom{3}{1}(4x)^2y^1 + \binom{3}{2}(4x)^1y^2 + \binom{3}{3}(4x)^0y^3$$

Simplifying, we get $$64x^3 + 48x^2y + 12xy^2 + y^3$$

Therefore, the correct option is (C).

Expand Using the Binomial Theorem (4x+y)3( 4 x + y ) ^ { 3 }(4x+y)3

Expand Using the Binomial Theorem $( 4 x + y ) ^ { 3 }$