Question

Expand the following:

`(x/2 - (3y)/5 + z)^2`

Answer 1

Given: `(x/2 - (3y)/5 + z)^2`

Step-wise calculation:

Use the expansion formula for (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca, where `a = x/2, b = -(3y)/5` and c = z.

1. Square each term:

`a^2 = (x/2)^2`

`a^2 = x^2/4`

`b^2 = (-(3y)/5)^2`

`b^2 = (9y^2)/25`

c² = z²

2. Calculate the cross terms with coefficients of 2: 

`2ab = 2 xx x/2 xx (-(3y)/5)`

`2ab = - (3xy)/5`

`2bc = 2 xx (-(3y)/5) xx z`

`2bc = -(6yz)/5`

`2ca = 2 xx z xx x/2`

2ca = xz

3. Put all terms together:

`(x/2 - (3y)/5 + z)^2 = x^2/4 + (9y^2)/25 + z^2 - (3xy)/5 - (6yz)/5 + xz`