Question

If the sum and difference of two numbers is 20 and 8 respectively, then the difference between their squares shall be:

• A. 56
• B. 160
• C. 28
• D. 180
• E. 12

Hint:

Difference of squares formula: $a^2 - b^2 = (a-(b)(a+(b)$. Use this to avoid calculating squares individually.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Apply algebraic identities to avoid calculating the individual numbers.
Step 2: Key Formula or Approach:
Difference of squares: \( x^2 - y^2 = (x + y)(x - y) \).
Step 3: Detailed Explanation:
1. Given: \( x + y = 20 \) and \( x - y = 8 \).
2. Difference between squares = \( x^2 - y^2 \).
3. Using the formula: \( (20) \times (8) = 160 \).
Step 4: Final Answer:
The difference between their squares is 160.