If 3x - 2y=5 then, prove that

27x^3 - 8y^3 - 54x^2y + 36xy^2 = 125

Step-by-step explanation:

(3x-2y) ³=5³

(3x) ³-3 (3x) ².2y+3.3x. (2y) ² - (2y) ³=125

27x³-54x²y+36y²x-8y³=125

see explanation

Step-by-step explanation:

Using the expansion

(a - b) ³ = a³ - b³ - 3ab (a - b) on the left side

with a = 3x and b = 2y, then

(3x - 2y) ³

= (3x) ³ - (2y) ³ - 3 (3x) (2y) (3x - 2y), that is

= 27x³ - 8y³ - 18xy (3x - 2y) ← distribute

= 27x³ - 8y³ - 54x²y + 36xy²

Thus given

3x - 2y = 5 ← cube both sides

(3x - 2y) ³ = 5³, hence

27x³ - 8y³ - 54x²y + 36xy² = 125 ← as required