Its Very Simple

Here is the solution for you...

f(x) = ax^4 - 4x^2 + ax - 3
Therefore,
f(b) = ab^4 - 4b^2 + ab - 3
and
f(-b) = ab^4 - 4b^2 -ab - 3

Now f(b) - f(-b) = 2ab

You can see except ab all the terms would cancel out.

So answer is (B).

I follow you up to the last step. f(-b) = ab^4 - 4b^2 -ab - 3 but shouldnt it be
f(-b) = a(-b)^4 - 4(-b)^2 -a(-b) - 3 . WIth all this, I am getting 2ab-6. Thanks for the explanation. I am understanding much better and am stuck on last detail. Was very tired when studying last night!

resilient wrote:I follow you up to the last step. f(-b) = ab^4 - 4b^2 -ab - 3 but shouldnt it be
f(-b) = a(-b)^4 - 4(-b)^2 -a(-b) - 3 . WIth all this, I am getting 2ab-6. Thanks for the explanation. I am understanding much better and am stuck on last detail. Was very tired when studying last night!

Since f(b) – f(-b), you're negating the second half of the equation, and the -3 changes to a +3... and both of the 3 cancels to 0.

resilient wrote:I follow you up to the last step. f(-b) = ab^4 - 4b^2 -ab - 3 but shouldnt it be
f(-b) = a(-b)^4 - 4(-b)^2 -a(-b) - 3 . WIth all this, I am getting 2ab-6. Thanks for the explanation. I am understanding much better and am stuck on last detail. Was very tired when studying last night!

Look the original equation is:

f(x) = ax^4 - 4x^2 + ax - 3

So, when you replace x with -b in left hand side, the same you need to do at the right hand side.

f(b) = a(-b)^4 - 4(-b)^2 + a(-b) - 3

But the equation you mentioned is

resilient wrote: f(-b) = a(-b)^4 - 4(-b)^2 -a(-b) - 3 .

Check here you have changed the sign of coefficient of term x. It should be +a instead of -a.

That's why you are getting incorrect answer.

I hope, now it must be clear to you.

resilient wrote:If f(x) = ax^4 - 4x^2 + ax - 3, then f(b) - f(-b) will equal:

A. 0
B. 2ab
C. 2ab^4 - 8b^2 - 6
D. -2ab^4 + 8b^2 + 6
E. 2ab^4 - 8b^2 + 2ab - 6

Since f(x) = ax^4 - 4x^2 + ax - 3, we know:

f(b) = ab^4 - 4b^2 + ab - 3 and:

f(-b) = a(-b)^4 - 4(-b)^2 + a(-b) - 3 = ab^4 - 4b^2 - ab - 3 and finally:

f(b) - f(-b) = (ab^4 - 4b^2 + ab - 3) - (ab^4 - 4b^2 - ab - 3) = 2ab

Answer:B