IF 2x + 5y =12, xy = 2, find the value of: $$8x^3+125y^3$$​​

Given:
2x + 5y = 12, xy = 2
Formula used:
a³+b³=(a+b)(a²-ab+b²)
Solution:
a = 2x
b = 5y
we have ;
8x³+125y^3​ = (2x)³+(5y)³ 

Comparing with a+b
a + b = 2x + 5y = 12
Calculate ab
ab = (2x)(5y) = 10xy
we know xy = 2
ab = 10 $$\times$$​ 2 = 20
To find a²-ab+b² we first calculate a²+b²
a²+b²= (a+b)²- 2ab
(a+b)²= 12²= 144
2ab = 2$$\times$$​20 = 40
Now,
a²+b²= 144 - 40 = 104
Now we can find a²- ab + b²
a²-ab + b² = a²+b²- ab = 104 - 20 = 84
Substituting back into the sum of cubes formula:
8x³+ 125y³= (a + b)(a²- ab + b²) =12 $$\times$$​ 84
= 1008​​​​​​