Question

You are given the expression 4−16=(2−4)(2+4) . Which polynomial identity describes the above numerical relationship?


A).n^2+4^2=(n−4)(n+4)

B).n^2−4^2=(n−4)(n+4)

C).4^2+n^2=(2+n)(4−n+n^2)

D).2^2−n^2=(4−n)(4+n)

Answer 1

In order to factorize this, we will use the distributive property which means to multiply each of the terms in the next factor.


So, (2x2)+(2x4)+(-4x2)+(-4x4)
4+8-8-16=-12

As we can see, that the two 8s cancel each other leaving us with 4-16


Response B best resembles this relationship. If we use the distributive property here, we get (nxn)+4n-4n-16
Leaving us with, n^2-16

To check, we can substitute n for 2 and check if we get -12