Question

निम्न व्यंजकों के गुणनखण्ड ज्ञात कीजिए

(i) 25x² + 10xy – 8y²

(ii) 4x² + 20xy + 25y²

Answer 1

(i) 25x² + 10xy – 8y² = 25x² + (20 – 10)xy – 8y² 

(∵ 25 × 8 = 200 = 2 × 2 × 2 × 5 × 5)

= 25x² + 20xy – 10xy – 8y² 

= 5x(5x + 4y) – 2y(5x + 4y)

= (5x + 4y)(5x – 2y)

(ii) 4x² + 20xy + 25y² 

= 4x² + (10 + 10)xy + 25y² 

(∵ 4 × 25 = 100 = 10 × 10)

= 4x² + 10xy + 10xy + 25y² 

= 2x(2x + 5y) + 5y (2x + 5y)

= (2x + 5y)(2x + 5y)