It is written as {(x-1)²} ^7 which is equal to (x-1)^14 since now n=14 the no of terms will be n+1 that is 15 terms

The expansion of (1-2x x^2)^7

To find the number of terms in the expansion of (1-2x x^2)^7, we need to understand the concept of the binomial theorem and combinatorics. The binomial theorem allows us to expand a binomial expression raised to a positive integer power. In this case, we have (1-2x x^2) raised to the power of 7.

Binomial Theorem:
The binomial theorem states that for any positive integer n,
(a + b)^n = C(n,0)a^n + C(n,1)a^(n-1)b + C(n,2)a^(n-2)b^2 + ... + C(n,n-1)ab^(n-1) + C(n,n)b^n

Where C(n,r) represents the binomial coefficient, which is the number of ways to choose r elements from a set of n elements.

Steps to determine the number of terms:
1. Determine the value of n: In this case, n is 7 since we have (1-2x x^2)^7.
2. Calculate the binomial coefficient for each term: The binomial coefficient C(n,r) represents the number of ways to choose r elements from a set of n elements.
3. Determine the maximum value of r: The maximum value of r in this case is n, which is 7.
4. Calculate the number of terms: The number of terms in the expansion of (1-2x x^2)^7 is equal to the maximum value of r + 1.

Calculations:
1. Determine the value of n: n = 7.
2. Calculate the binomial coefficient for each term: We need to calculate C(7,0), C(7,1), C(7,2), ..., C(7,7).
- C(7,0) = 1
- C(7,1) = 7
- C(7,2) = 21
- C(7,3) = 35
- C(7,4) = 35
- C(7,5) = 21
- C(7,6) = 7
- C(7,7) = 1
3. Determine the maximum value of r: The maximum value of r is 7.
4. Calculate the number of terms: The number of terms in the expansion is 7 + 1 = 8.

Conclusion:
The expansion of (1-2x x^2)^7 has a total of 8 terms.