Question

Use the binomial theorem to determine the expanded form of the binomial expression

(
x
+
y
)
4
.


x
4
+
y
4

x
4
+
4
⁢
x
3
⁢
y
+
6
⁢
x
2
⁢
y
2
+
4
⁢
x
⁢
y
3
+
y
4

Answer 1

Explanation:

Expand Using the Binomial Theorem (X+Y)^4 (X + Y)4 ( X + Y) 4 Use the binomial expansion theorem to find each term. The binomial theorem states (a+b)n = n ∑ k=0nCk⋅(an−kbk) ( a + b) n = ∑ k = 0 n n C k ⋅ ( a n - k b k). 4 ∑ k=0 4! (4− k)!k! ⋅(X)4−k ⋅(Y)k ∑ k = 0 4 4! ( 4 - k)! k! ⋅ ( X) 4 - k ⋅ ( Y) k Expand the summation. 4! (4−0)!0!