Write the following in expanded form: `(x-2y-3z)^2` (ii) `(-x+2y+z)^2`

Explanation

(i) `(x-2y-3z)^2`
Using the identity, `(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca`:
`= [x²+(-2y)+(-3z)]^2`
`= x^2+(-2y)^2+(-3z)^2+2x(-2y)+2(-2y)(-3z)+2(-3z)x`
`= x^2+4y^2+9z^2-4xy+12yz-6xz`
`therefore (x-2y-3z)^2`
`=x^2+4y^2+9z^2-4xy+12yz-6xz`

(ii) `(-x+2y-3z)^2`
Using the algebraic identity `(a+b+c)^2= a^2+b^2+c^2+2ab+2bc+2ca`:
`=(-x)^2+(2y)^2+(-3z)^2+2(-x)(2y)+2(2y)(-3z)+2(-3z)(-x)`
`=x^2+4y^2+9z^2-4xy-12yz+6xz`
`therefore (-x+2y-3z)^2=x^2+ 4y^2+ 9z^2-4xy-12yz+6zx`