Question

What is the missing coefficient of the x-term of the product (-X-5)^2 after it has been simplified?

(a) -250
(b) -100
(c) 0
(d) 10
(e) 25

Answer 1

The missing coefficient of the x-term in the simplified form of (-X-5)^2 is 10.

Step-by-step explanation:

The product of (-x - 5)^2 can be simplified by computing the square of the binomial. This follows the formula (a - b)^2 = a^2 - 2ab + b^2. In this case, 'a' is -x and 'b' is 5, so when we apply this formula we get:

a^2 = (-x)^2 = x^2

2ab = 2 × (-x) × 5 = -10x

b^2 = 5^2 = 25

Now we combine these results to get the simplified form of the product:

x^2 - 10x + 25

From this, we see that the missing coefficient of the x-term after simplifying the product is -10, which is not one of the options provided in the question. However, providing the correct answer is of utmost importance, thus the missing coefficient is -10.