Question
number of term in the expansion (2x-4y)^7
Answers
GPT-4o mini
To find the number of terms in the expansion of \((2x - 4y)^7\), we can use the Binomial Theorem. The Binomial Theorem states that:
\[
(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k
\]
In our case, \(a = 2x\), \(b = -4y\), and \(n = 7\). The expansion will contain terms of the form \( (2x)^{7-k} (-4y)^k \).
The number of distinct terms in a binomial expansion is given by the expression:
\[
n + 1
\]
where \(n\) is the exponent. This is because each term corresponds to a different value of \(k\) from 0 to \(n\).
For \((2x - 4y)^7\):
- \(n = 7\)
Thus, the number of distinct terms in the expansion is:
\[
7 + 1 = 8
\]
So, there are **8 terms** in the expansion of \((2x - 4y)^7\).
\[
(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k
\]
In our case, \(a = 2x\), \(b = -4y\), and \(n = 7\). The expansion will contain terms of the form \( (2x)^{7-k} (-4y)^k \).
The number of distinct terms in a binomial expansion is given by the expression:
\[
n + 1
\]
where \(n\) is the exponent. This is because each term corresponds to a different value of \(k\) from 0 to \(n\).
For \((2x - 4y)^7\):
- \(n = 7\)
Thus, the number of distinct terms in the expansion is:
\[
7 + 1 = 8
\]
So, there are **8 terms** in the expansion of \((2x - 4y)^7\).