The value of (a + b)² + (a - b)² is
(a) 2a + 2b
(b) 2a - 2b
(c) 2a² + 2b²
(d) 2a² - 2b²

Solution:

Correct option is (c).

Given, (a + b)² + (a - b)²

We have standard identities, (a + b)² = a² + 2ab + b² and (a - b)² = a² - 2ab + b²

∴ (a + b)² + (a - b)² = a² + 2ab + b² + a² - 2ab + b²

= 2a² + 2b²

✦ Try This: The value of (a + b)² -  (a - b)² is (a) 4, (b) ab, (c) 4ab, (d) - 4ab

Correct option is(c)

Given, (a + b)² - (a - b)²

We have standard identities, (a + b)² = a² + 2ab + b² and (a - b)² = a² - 2ab + b²

∴ (a + b)² + (a - b)²      = a² + 2ab + b² - [ a² - 2ab + b²]

= a² + 2ab + b² - a² + 2ab - b²            

= 4ab 

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 9

NCERT Exemplar Class 8 Maths Chapter 7 Problem 32

The value of (a + b)² + (a - b)² is (a) 2a + 2b, (b) 2a - 2b, (c) 2a² + 2b², (d) 2a² - 2b²

Summary:

The value of (a + b)² + (a - b)² is 2a² + 2b²

☛ Related Questions:

• The value of (a + b)² - (a - b)² is (a) 4ab (b) – 4ab (c) 2a² + 2b² (d) 2a² - 2b²
• The product of two terms with like signs is a ____________ term
• The product of two terms with unlike signs is a ___________ term