Examine whether the following equations are quadratic equations or not:

(2x + 3)² — (3x + 2)² = 13

Using the identity (a + b)(a – b) = a² – b²

Where a = (2x + 3) and b = (3x + 2)

⇒ [(2x + 3) + (3x + 2)] × [(2x + 3) – (3x + 2)] = 13

⇒ (5x + 5) × [2x + 3 – 3x – 2] = 13

⇒ (5x + 5) × (1 – x) = 13

⇒ 5x – 5x² + 5 – 5x = 13

⇒ – 5x² + 5 – 13 = 0

⇒ – 5x² + 0x – 8 = 0

Comparing equation – 5x² + 0x – 8 = 0 with ax² + bx + c = 0 we get

a = – 5, b = 0 and c = – 8

Here a, b, c ∈ R and a ≠ 0

The degree of polynomial – 5x² + 0x – 8 = 0 is 2

Hence (2x + 3)² — (3x + 2)² = 13 is a quadratic equation