Concept: This problem uses the algebraic identity for the difference of two squares: . Step 1: Identify the pattern on the right-hand side (RHS) of the equation
The right-hand side of the equation is .
This is in the form , where:
Step 2: Apply the difference of squares identity
Using the identity :
Step 3: Simplify the squared terms
So, the RHS becomes:
Step 4: Equate the given equation with the simplified RHS
The given equation is .
We found that the RHS simplifies to .
Therefore, we have:
Step 5: Solve for b
For this equality to hold true for all values of , the corresponding terms must be equal.
Comparing the constant terms on both sides (or subtracting from both sides):
Multiplying both sides by -1:
The value of b is . This matches option (3).