Question

Expand the following:

`((3x)/4+(2y)/5)^3`

Answer 1

Using the identity:

(a + b)³ = a³ + 3a²b + 3ab² + b³

Here, let `a = (3x)/4,b = (2y)/5`

`((3x)/4 + (2y)/5)^3 = ((3x)/4)^3 + 3((3x)/4)^2((2y)/5) + 3((3x)/4)((2y)/5)^2 + ((2y)/5)^3`

= `((3^3x^3)/4^3) + 3((9x^2)/16)((2y)/5) + 3((3x)/4)((4y^2)/25) + ((2^3y^3)/5^3)`

= `(27x^3)/64 + 3((18x^2y)/80) + 3((3xy^2)/25) + (8y^3)/125`

= `(27x^3)/64 + 3((9x^2y)/40) + (9xy^2)/25 + (8y^3)/125`

∴ `((3x)/4 + (2y)/5)^3 = (27x^3)/64 + (27x^2y)/40 + (9xy^2)/25 + (8y^3)/125`