Question

Expand the following:

`(1/3x + 1/2y)^2`

Answer 1

Given: `(1/3x + 1/2y)^2`

Step-wise calculation using the identity (a + b)² = a² + 2ab + b²:

1. Square the first term:

`(1/3 x)^2 = 1/9 x^2`

2. Square the second term:

`(1/2 y)^2 = 1/4 y^2`

3. Calculate twice the product of the two terms:

`2 xx 1/3 x xx 1/2 y = 2 xx 1/6 xy`

`2 xx 1/3 x xx 1/2 y = 1/3 xy`

Combine all parts:

`(1/3x + 1/2y)^2 = 1/9 x^2 + 1/4 y^2 + 1/3 xy`