Simplify: (3x + 2y)² + (3x - 2y)²
Solution:
Given, (3x + 2y)² + (3x - 2y)²
Using standard identities: (a + b)² = a² + 2ab + b² and (a - b)² = a² - 2ab + b²
Here, a = 3x and b = 2y
(3x + 2y)² + (3x - 2y)²
= [(3x)² + 2(3x)(2y) + (2y)²] + [(3x)² - 2(3x)(2y) + (2y)²]
= [9x² + 12xy + 4y²] + [9x² - 12xy + 4y²]
= 9x² + 9x² + 12xy - 12xy + 4y² + 4y²
= 18x² + 8y²
✦ Try This: Simplify: (5p + 3q)² + (5p - 3q)²
Given, (5p + 3q)² + (5p - 3q)²
Using standard identities: (a + b)² = a² + 2ab + b² and (a - b)² = a² - 2ab + b²
Here, a = 5p and b = 3q
(5p + 3q)² + (5p - 3q)²
= [(5p)² + 2(5p)(3q) +(3q)²] + [(5p)² - 2(5p)(3q) +(3q)²]
=25p² + 30pq + 9q² + 25p² - 30pq + 9q²
= 50p² + 18q²
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 9
NCERT Exemplar Class 8 Maths Chapter 7 Problem 84(i)
Simplify: (3x + 2y)² + (3x - 2y)²
Summary:
Simplifying (3x + 2y)² + (3x - 2y)² we get, 18x² + 8y²
☛ Related Questions:
visual curriculum