(4x + 1/3y)^3 = (4x + 1/3y)(4x + 1/3y)(4x + 1/3y)
Expanding this expression, we get:
= (4x 4x 4x) + (4x 4x 1/3y) + (4x 1/3y 4x) + (4x 1/3y 1/3y)
= 64x^3 + 32x^2/3y + 32x^2/3y + 8x * 1/9y^2
= 64x^3 + 64x^2/3y + 8x/9y + 4/9y^2 + 1/27y^3
So, (4x + 1/3y)^3 = 64x^3 + 64x^2/3y + 8x/9y + 4/9y^2 + 1/27y^3.
(4x + 1/3y)^3 = (4x + 1/3y)(4x + 1/3y)(4x + 1/3y)
Expanding this expression, we get:
= (4x 4x 4x) + (4x 4x 1/3y) + (4x 1/3y 4x) + (4x 1/3y 1/3y)
(1/3y 4x 4x) + (1/3y 4x 1/3y) + (1/3y 1/3y 4x) + (1/3y 1/3y 1/3y)= 64x^3 + 32x^2/3y + 32x^2/3y + 8x * 1/9y^2
32x^2/3y + 4x/9y + 4x/9y + 1/27y^3= 64x^3 + 64x^2/3y + 8x/9y + 4/9y^2 + 1/27y^3
So, (4x + 1/3y)^3 = 64x^3 + 64x^2/3y + 8x/9y + 4/9y^2 + 1/27y^3.