1.

निम्न व्यंजकों के गुणनखण्ड ज्ञात कीजिए(i) 25x2 + 10xy – 8y2(ii) 4x2 + 20xy + 25y2

Answer»

(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)



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