Question

Expand the following:

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

Answer 1

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

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

1. `a = 2x` and `b = 1/3 y`

2. Square of first term:

(2x)² = 4x²

3. Twice the product of the two terms:

`2 xx 2x xx 1/3 y = 4/3 xy`

4. Square of the second term:

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

5. Combine with subtraction because of the minus sign:

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