(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?
No 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.