Explanation

Quantity A to find \(-10a - a^2 - 100 - 10a\), or \(-a2 - 20a - 100\).

Anything other than zero to an even power is positive, so \(-a^2\) is negative.

A negative number minus a positive number (20a) will remain negative.

A negative minus 100 will be even more negative.

So, Quantity A must be negative, and it must be less than Quantity B. The answer is choice (B).

Alternatively, plugging in a few positive values for a will give you, in the parentheses: (negative) times (positive) = negative for Quantity A, except if a = 10, which yields 0 for Quantity A. But Quantity A is still less than Quantity B.
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