Question

Use the binomial theorem to expand each of the following:
(1-x)⁵

Answer 1

The binomial theorem allows us to expand expressions in the form of (a + b)^n. In this case, we can expand (1 - x)^5 as 1 - 5x + 10x^2 - 10x^3 + 5x^4 - x^5.

Step-by-step explanation:

The binomial theorem allows us to expand expressions in the form of (a + b)^n. In this case, we have (1 - x)^5. Using the binomial theorem formula, we can expand it as follows:

(1 - x)^5 = 1C0 * 1^5 * (-x)^0 + 5C1 * 1^4 * (-x)^1 + 5C2 * 1^3 * (-x)^2 + 5C3 * 1^2 * (-x)^3 + 5C4 * 1^1 * (-x)^4 + 5C5 * 1^0 * (-x)^5

Simplifying the equation:

(1 - x)^5 = 1 - 5x + 10x^2 - 10x^3 + 5x^4 - x^5