Select a suitable identity and find the following products(i) (7d –

1.	Select a suitable identity and find the following products(i) (7d – 9e)(7d – 9e)(ii) (m2 – n2)(m2 + n2)
Answer» i) (7d – 9e) (7d – 9e) = (7d – 9e)² is in the form of (a – b)². = (7d)² – 2 × 7d × 9e + (9e)² [ ∵ (a – b)² = a² – 2ab + b²] = 7d × 7d – 126de + 9e × 9e = 49d² – 126de + 81e² ii) (m² – n²) (m² + n²) is in the form of (a + b) (a – b). ∴ (a + b) (a – b) = a² – b² ∴ (m² + n²) (m² – n²) = (m²)² – (n²)² = m⁴ – n⁴

Select a suitable identity and find the following products(i) (7d – 9e)(7d – 9e)(ii) (m2 – n2)(m2 + n2)

Answer»

i) (7d – 9e) (7d – 9e)

= (7d – 9e)² is in the form of (a – b)².

= (7d)² – 2 × 7d × 9e + (9e)² [ ∵ (a – b)² = a² – 2ab + b²]

= 7d × 7d – 126de + 9e × 9e

= 49d² – 126de + 81e²

ii) (m² – n²) (m² + n²) is in the form of (a + b) (a – b).

∴ (a + b) (a – b) = a² – b²

∴ (m² + n²) (m² – n²) = (m²)² – (n²)² = m⁴ – n⁴