(4x + 4) (ax - 1) - x² + 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?

The correct answer is: -3

○        The concept used in this question is of algebraic expressions or expressions.
○        The algebraic expression is any mathematical statement. It is consists of numbers, variables and an arithmetic operation between them.
○        Expressions do not have fixed value.
○        The value can be get by just putting number is place of variables.

• Step by step explanation:

○        Given:
(4x + 4) (ax - 1) - x² + 4 = bx
a and b are constant.
○        Step 1:
○        Simplify the expression.
(4x + 4) (ax - 1) - x² + 4 = bx
4x (ax - 1) + 4 (ax - 1) - x² + 4 = bx
4ax² - 4x + 4ax - 4 -x² + 4 = bx
Arrange in decreasing order of power of coefficient
4ax² -x² - 4x + 4ax + 4 + 4 = bx
(4a - 1)x² + (-4 + 4a)x + 8 = bx
○        Step 1:
○        Compare both the side.
We can see that left hand side do not have term with x²
∴ (4a - 1) = 0
4a = 1
a =
And,
(-4 + 4a) = b
-4 + 4 = b
-4 + 1 = b
-3 = b
Hence, the b is equal to -3.

• Final Answer:

Correct option is,
Option B. -3.