Question

(6.25p^2 – 2.25q^2) / (2.5p + 1.5q)​

Answer 1

Answer:

the identities

(a + b) 2 = a2 + b2 + 2ab

(a – b) 2 = a2 + b2 – 2ab

(2.5p – 1.5q)2 – (1.5p – 2.5q)2

Consider (4m + 5n)2

Using identity

(a – b) 2 = a2 + b2 – 2ab

(2.5p – 1.5q)2 = (2.5p)2 + (1.5q)2 – 2 × (2.5p) × (1.5q)

(2.5p – 1.5q)2 = 6.25p2 + 2.25q2 – 7.5pq………………………….(1)

Consider (1.5p – 2.5q)2

Using identity

(a – b) 2 = a2 + b2 – 2ab

(1.5p – 2.5q)2 = (1.5p)2 + (2.5q)2 – 2 × (1.5p) × (2.5q)

(1.5p – 2.5q)2 = 2.25p2 + 6.25q2 – 7.5pq………………………….(1)

(2.5p – 1.5q)2 + (1.5p – 2.5q)2 = 6.25p2 + 2.25q2 – 7.5pq – (2.25p2 + 6.25q2 – 7.5pq)

(2.5p – 1.5q)2 + (1.5p – 2.5q)2 = 6.25p2 + 2.25q2 – 7.5pq – 2.25p2 – 6.25q2 + 7.5pq

(2.5p – 1.5q)2 + (1.5p – 2.5q)2 = 6.25p2 – 2.25p2 + 2.25q2 – 6.25q2 – 7.5pq + 7.5pq

(2.5p – 1.5q)2 + (1.5p – 2.5q)2 = 4p2 – 4q2