Question

Find the value of the expression

{(A + B)² - (A - B)²}/AB 

1. 4
2. 6
3. 8
4. 2

Answer 1

Correct Answer - Option 1 : 4

Given:

{(A + B)2 - (A - B)2}/AB 

Formula used:

(A + B)² = A² + B² + 2AB

(A - B)² = A² + B2 - 2AB

Calculation:

Subtracting both formula

⇒ (A + B)² - (A - B)² = A2 + B2 + 2AB - (A2 + B2 - 2AB)

⇒ (A + B)2 - (A - B)² = A2 + B2 + 2AB - A² - B² + 2AB

⇒ (A + B)2 - (A - B)² = 4AB

∴ {(A + B)2 - (A - B)²}/AB = 4