Use the Binomial Theorem to expand and simplify the expression. $( 4 x + 5 y ) ^ { 4 }$
A) $256 x ^ { 4 } + 1280 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } + 625 y ^ { 4 }$
B) $256 x ^ { 4 } + 1280 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } - y ^ { 4 }$
C) $256 x ^ { 4 } + 320 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } + 625 y ^ { 4 }$
D) $256 x ^ { 4 } + 500 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } - 625 y ^ { 4 }$
E) $x ^ { 4 } + 1280 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } + y ^ { 4 }$

Question

Quizplus · Accepted Answer

The Binomial Theorem states that $(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k}b^k$. Applying this to $(4x + 5y)^4$, we calculate each term: $256x^4$, $1280x^3y$, $2400x^2y^2$, $2000xy^3$, and $625y^4$, matching option A.

Use the Binomial Theorem to Expand and Simplify the Expression (4x+5y)4( 4 x + 5 y ) ^ { 4 }(4x+5y)4

Use the Binomial Theorem to Expand and Simplify the Expression $( 4 x + 5 y ) ^ { 4 }$