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

Question

asked Jul 15, 2023 147k views

1 Answer

Stefan Mesken · Answer 1 · 2023-07-19T17:32:29+0000

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

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