(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) 12

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 bx, then that means the x^2 and constant terms must all cancel out. Because there’s a -x^2 outside the (4x+4)(ax-1), we know that 4x\times ax must result in a positive x^2 to cancel it out. So let’s see what happens when we plug in \frac{1}{4} for a.


There you have it. If the whole expression simplifies to only an x term, then a must be \frac{1}{4}. Plugging that in for a leaves you with –3 for b.

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