Applying the Binomial Theorem
Algebra · Flashcards · Recall
ALGEBRA · FLASHCARDS
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QUESTION
In
(
x
+
y
)
n
(x+y)^n
(
x
+
y
)
n
, what is the exponent of
x
x
x
in the term containing
y
k
y^k
y
k
?
QUESTION
What are the values of
(
n
0
)
\binom{n}{0}
(
0
n
)
and
(
n
n
)
\binom{n}{n}
(
n
n
)
for any positive integer
n
n
n
?
QUESTION
State the Binomial Theorem formula for expanding
(
x
+
y
)
n
(x+y)^n
(
x
+
y
)
n
using binomial coefficients.
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ANSWER
(
x
+
y
)
n
=
∑
k
=
0
n
(
n
k
)
x
n
−
k
y
k
(x+y)^n=\sum_{k=0}^{n}\binom{n}{k}x^{n-k}y^k
(
x
+
y
)
n
=
∑
k
=
0
n
(
k
n
)
x
n
−
k
y
k
. The general formula for binomial expansion with coefficients and powers.
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