If a is a negative, odd number, b is a positive, odd number, and c is a negative, even number, then (ab)^2 + c^2 will be which of the following:

Question

A. positive odd

B. positive even

C. negative odd

D. negative even

I cannot figure out if the negative component of c would also be squared, making it a positive number, or if the negative is not squared because it is not in parentheses.

Answer 1

First, to help you "figure out" the sign of c², for example, if c = (-1), then +(-1)(-1) = 1.

Also, all squares are positive. This applies to c² and to (ab)². Let's get that out of the way and limit the possible answers to either A or B.

Now, we may concentrate on odd/even.

1. Since c is even, c² is even.
2. Since a is odd and b is odd, then ab is odd. Since ab is odd, (ab)² is odd. [note: if 2 is not a factor of a and 2 is not a factor of b, then 2 is not a factor of a*b and 2 is not a factor of a*a*b*b.].

What, then, is odd + even? You may consider the fact that odd numbers are always an even distance apart. odd + even = odd

Answer A.

Answer 2

ab : negative times positive is negative and odd times odd is odd

ab is a negative odd number

(ab)^2 is negative odd times negative odd which equals a positive odd (negative times negative is positive)

c^2 : negative times negative is positive and even times even is even

c^2 is a positive even number

positive plus positive equals positive

odd plus even equals odd

positive odd plus positive even equals positive odd

A. is the answer

c^2 means that the "-" and the numeral both are squared because you have a variable

if you had a specific number like -4 and it was -4^2, then only the 4 would be squared and you would get

-4^2=-16 because you raise to a power before you subtract or take the opposite

however, (-4)^2=(-4)(-4)=+16

Answer 3

(ab)^2 + c^2

It will be A. Positive Odd.

Let a = -1

Let b = 1

Let c = -2

Then (-1x1)² + (-2)² = 1 + 4 = 5 = Positive ODD

Answer 4

Answer 5

Since a and b are both odd numbers, their product will even. Since we are squaring ab, it will be positive, regardless. Since c is an even number the square will be even. Since we are squaring c, it will also be positive. The sum of two positive event terms will be positive even (B).