Question

What is the coefficient of x^6 in the expansion of (x 5)^10?

Answer 1

The coefficient of x^6 in the expansion of (x+5)^10 can be calculated using the binomial expansion theorem.

Step-by-step explanation:

The expansion of (x+5) raised to the power of 10 can be found using the binomial expansion theorem. The coefficient of x^6 in this expansion can be calculated using the formula:

Coefficient = 10C6 * (x)^6 * (5)^4

Using the formula, we substitute the values of 10C6 = 210, (x)^6 and (5)^4 into the formula to calculate the coefficient of x^6.

Answer 2

The coefficient of x^6 in the expansion of (x + 5)^10 is found using the binomial theorem. The computation shows that it is 210 × 625, resulting in a coefficient of 131,250.

Step-by-step explanation:

The student is asking about finding the coefficient of x6 in the binomial expansion of (x + 5)10. To solve this, we can use the binomial theorem, which states that the binomial coefficients in the expansion of (a + b)n are given by the formula nCr where r is the term index.

For the x6 term in the expansion of (x + 5)10, the term is represented as 10C4 × x6 × 54. Calculating 10C4, which is the number of ways to choose 4 items out of 10, we get 210. Therefore, the coefficient is 210 × 54, which is 210 × 625.

So, the coefficient of x6 in the expansion of (x + 5)10 is 210 × 625, which equals 131,250.