the number of terms in the expansion (x+a)^9=
Answers
Step-by-step explanation:
(x+a)
47
−(x−a)
47
When we expand the above equation using binomial expansion
(x+y)
n
=(
k=0
∑
n
n
C
k
x
k
y
n−k
)
So the above equation becomes
(x+a)
47
=(
k=0
∑
47
47
C
k
x
k
a
47−k
)
(x−a)
47
=(
k=0
∑
47
47
C
k
x
k
(−a)
47−k
)
(x+a)
47
⇒There are 48 terms in the expansion and all are positive
(x−a)
47
⇒There are 48 terms in the expansion
The terms with odd powers of a will be cancelled and those with even powers of a will add up.
24 terms will be positive and 24 negative in the expansion of (x−a)
47
48 terms positive-[24 terms negative and 24 terms positive]
=48termspositive+24termsnegative+24termspositive
=24 terms
PLS MARK AS BRAINLIST
Answer:
(x+a)
47
−(x−a)
47
When we expand the above equation using binomial expansion
(x+y)
n
=(
k=0
∑
n
n
C
k
x
k
y
n−k
)
So the above equation becomes
(x+a)
47
=(
k=0
∑
47
47
C
k
x
k
a
47−k
)
(x−a)
47
=(
k=0
∑
47
47
C
k
x
k
(−a)
47−k
)
(x+a)
47
⇒There are 48 terms in the expansion and all are positive
(x−a)
47
⇒There are 48 terms in the expansion
The terms with odd powers of a will be cancelled and those with even powers of a will add up.
24 terms will be positive and 24 negative in the expansion of (x−a)
47
48 terms positive-[24 terms negative and 24 terms positive]
=48termspositive+24termsnegative+24termspositive
=24 terms