Question

Expand the following using the suitable identity.(-x + 2y - 3z)^2

Answer 1

`x^2+4y^2+9z^2-4xy+6xz_{}-12yz`

Explanations:

Given the expression (-x + 2y - 3z)², we are to expand it using a suitable identity.

Using the square of the sum of trinomial identity expressed as:

`(a+b+c)^2=a^2+b^2+c^2+2\text{ab+2ac+2bc}`

From the given expression;

`\begin{gathered} a=-x \\ b=2y \\ c=-3z \end{gathered}`

Substitute the parameters into the identity to expand as shown:

`(-x+2y-3z)^2=(-x)^2+(2y)^2+(-3z)^2+2(-x)(2y)+2(-x)(-3z)_{}+2(2y)(-3z)`

Simplify the result to have:

`(-x+2y-3z)^2=x^2+4y^2+9z^2-4xy+6xz_{}-12yz`

This gives the correct expansion using a suitable identity