(4x + 4)(ax – 1) – x^2 + 4

In the expression above, a is a constant. If the expression is equivalent to bx, where b is a constant, what is the value of b?

A) -5

B) -3

C) 0

D) 12No idea how to solve this! I tried factoring this way and that, expanding, setting everthing on left in form of x (….) + 4 = bx, but no go. Help!

The trick is to recognize that if the expression simplifies to , then that means the and constant terms must all cancel out. Because there’s a outside the , we know that must result in a positive to cancel it out. So let’s see what happens when we plug in for *a*.

There you have it. If the whole expression simplifies to only an *x* term, then *a* must be . Plugging that in for *a* leaves you with –3 for *b*.