# 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:**

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