Question

Find the coefficient of the x^(3) term in (x-3)^(10)

Answer 1

The coefficient of the x³ term in (x-3)¹⁰ is -3240.

Step-by-step explanation:

To find the coefficient of the x³ term in (x-3)¹⁰, we can use the binomial theorem. According to the binomial theorem, the coefficient of the x³ term is given by the formula: C(n, r) * a^(n-r) * b^r, where C(n, r) is the binomial coefficient, a is the first term of the binomial, b is the second term of the binomial, n is the exponent of the binomial, and r is the power of the x-term you are interested in.

In this case, a = x, b = -3, n = 10, and r = 3. Plugging these values into the formula, we get: C(10, 3) * x^(10-3) * (-3)^3 = 120 * x^7 * (-27) = -3240x^7.

Therefore, the coefficient of the x³ term in (x-3)¹⁰ is -3240.

Answer 2

The coefficient of the x^3 term in (x-3)^10 is -3240.

To find the coefficient of the x^3 term in (x-3)^10, we can use the Binomial Theorem.

Binomial Theorem:

(a + b)^n = nC0 * a^n * b^0 + nC1 * a^(n-1) * b^1 + ... + nCn * a^0 * b^n

Applying the Theorem:

We have (x - 3)^10, where a = x, b = -3, and n = 10.

We want to find the coefficient of the x^3 term, which means we need to find the term with a^(10-3) * b^3 = x^7 * (-3)^3.

Relevant Term:

The term we need is: 10C3 * x^7 * (-3)^3

Calculating the Coefficient:

10C3 = 10! / (3! * 7!) = 120

(-3)^3 = -27

Coefficient:

120 * (-27) = -3240