Question

If y = 3, then y³(y³-y) =

• A. 300
• B. 459
• C. 648
• D. 999
• E. 1099

Hint:

When an expression has the same variable multiple times, calculate its powers first (like \( y^3 \)) and then substitute that value in all places to simplify the calculation.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This problem requires evaluating an algebraic expression by substituting a given value for the variable and following the order of operations (PEMDAS/BODMAS).
Step 2: Key Formula or Approach:
The order of operations is: 1. Parentheses (or Brackets) 2. Exponents (or Orders) 3. Multiplication and Division (from left to right) 4. Addition and Subtraction (from left to right)
Step 3: Detailed Explanation:
The expression is \( y^3(y^3-y) \), and we are given \( y = 3 \).
First, substitute 3 for y in the expression: \[ 3^3(3^3 - 3) \] Following the order of operations, we first evaluate the expression inside the parentheses. Inside the parentheses, we handle the exponent first.
\[ 3^3 = 3 \times 3 \times 3 = 27 \] Now substitute this back into the expression: \[ 27 \times (27 - 3) \] Next, complete the operation inside the parentheses: \[ 27 - 3 = 24 \] The expression simplifies to: \[ 27 \times 24 \] Now, perform the multiplication: \[ 27 \times 24 = 648 \] Step 4: Final Answer:
The value of the expression is 648. The correct option is (C).