Question

Simplity (4m - 5n)^2 (4m 5n)^2​

Answer 1

Answer:

41m2 + 41n2 + 80mn

Step-by-step explanation:

Using the identities

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

(a – b) 2 = a2 + b2 – 2ab

(4m + 5n)2 + (5m + 4n)2

Consider (4m + 5n)2

Using identity

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

(4m + 5n)2 = (4m)2 + (5n)2 + 2 × 4m × 5n

(4m + 5n)2 = 16m2 + 25n2 + 40mn…………………………..(1)

Consider (5m + 4n)2

Using identity

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

(5m + 4n)2 = (5m)2 + (4n)2 + 2 × 5m × 4n

(5m + 4n)2 = 25m2 + 16n2 + 40mn…………………………..(2)

(4m + 5n)2 + (5m + 4n)2 = 16m2 + 25n2 + 40mn + 25m2 + 16n2 + 40mn

(4m + 5n)2 + (5m + 4n)2 = 16m2 + 25m2 + 25n2 + 16n2 + 40mn + 40mn

(4m + 5n)2 + (5m + 4n)2 = 41m2 + 41n2 + 80mn