Question

Can anybody explain how to solve this?

Answer 1

@mww

Answer 2

Do I first find the GCF or..?

Answer 3

This one is a tricky one.
You need to notice that it's got 4 terms.
We can't use grouping in pairs since we don't get any common factors from that. So we need to group differently.
There is x and b as the variables. Watch what happens when I segregate the last three terms as a group...
\[16x ^{4} - b^4 +10b^2 - 25 = 16x^4 - (b^4 -10b^2 +25)\]
\[b^4 -10b^2 + 25 = (b^2 - 5)^2\]
So \[16x ^{4} - b^4 +10b^2 - 25 = 16x^4 - (b^4 -10b^2 +25) = 16x^4 - (b^2 -5)^2 = (4x^2)^2 - (b^2-5)^2\]
This becomes a difference of two squares.
\[(4x^2)^2 -(b^2-5)^2 = (4x^2 + (b^2 -5))(4x^2 - (b^2 -5)) = (4x^2 + b^2 -5)(4x^2 -b^2 +5)\]
Hence D.

Answer 4

What I did was expose a perfect square from the last three terms involving b to make a difference of two squares.

Answer 5

In any MCQ, if in doubt, you can expand and see which answer fits. It might take a while but MCQs allow you that luxury. Think about how you can regroup a question till it fits something familiar.

Answer 6

THANK YOU SO MUCH!!!