Find:(i)(9m – 2n)2(ii) (6pq – 7rs)2(iii) (5x2 – 6y2)2

1.	Find:(i)(9m – 2n)2(ii) (6pq – 7rs)2(iii) (5x2 – 6y2)2
Answer» i) (9m – 2n)² is in the form of (a – b)². (a – b)² = a² – 2ab + b² (9m – 2n)² = (9m)² – 2 × 9m × 2n + (2n)² = (9m × 9m) – 36mn + (2n × 2n) = 81m² – 36mn + 4n² ii) (6pq – 7rs)² a = 6pq, b = 7rs (6pq – 7rs)² = (6pq)² – 2 × 6pq × 7rs + (7rs)² = (6pq × 6pq) – 84pqrs + (7rs × 7rs) = 36p²q² – 84pqrs + 49r²s² iii) (5x² – 6y²)² = (5x²)² – 2 × 5x² × 6y² + (6y²)² = (5x² × 5x²) – 60x²y² + (6y² × 6y²) = 25x⁴ – 60x²y² + 36y⁴

Answer»

i) (9m – 2n)² is in the form of (a – b)².

(a – b)² = a² – 2ab + b²

(9m – 2n)² = (9m)² – 2 × 9m × 2n + (2n)²

= (9m × 9m) – 36mn + (2n × 2n)

= 81m² – 36mn + 4n²

ii) (6pq – 7rs)²

a = 6pq, b = 7rs

(6pq – 7rs)² = (6pq)² – 2 × 6pq × 7rs + (7rs)²

= (6pq × 6pq) – 84pqrs + (7rs × 7rs)

= 36p²q² – 84pqrs + 49r²s²

iii) (5x² – 6y²)² = (5x²)² – 2 × 5x² × 6y² + (6y²)²

= (5x² × 5x²) – 60x²y² + (6y² × 6y²)

= 25x⁴ – 60x²y² + 36y⁴

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