Final answer:
The first three terms in the expansion of (1 - x)^6 are found using the binomial theorem as follows: the first term is 1, the second term is -6x, and the third term is 15x^2. So, the correct answer is A) 1 - 6x + 15x^2.
Step-by-step explanation:
To find the first three terms, in ascending powers of x, in the expansion of (1 - x)^6, we use the binomial theorem. The binomial theorem expresses the expansion of a binomial raised to a power as a sum of terms involving the original binomial's coefficients.
The general form of the binomial theorem is (a + b)^n = a^n + (n choose 1)a^(n-1)b + (n choose 2)a^(n-2)b^2 + ..., where (n choose k) represents the binomial coefficient.
For the given binomial (1 - x)^6, applying the binomial theorem yields the following terms:
The first term (with x^0): (1)^6 = 1
The second term (with x^1): (6 choose 1)(1)^5(-x) = -6x
The third term (with x^2): (6 choose 2)(1)^4(-x)^2 = 15x^2
Therefore, the first three terms of the expansion in ascending powers of x are 1 - 6x + 15x^2.
Hence, the correct answer is Option A: 1 - 6x + 15x^2.