Question

If 3x - 2y=5 then, prove that
27x^3 - 8y^3 - 54x^2y + 36xy^2 = 125
​

Answer 1

see explanation

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

Answer 2

Explanation:

(3x-2y)³=5³

(3x)³-3(3x)².2y+3.3x.(2y)²-(2y)³=125

27x³-54x²y+36y²x-8y³=125