Expand the following
(i) `(4a-b+ac)^(2)` (ii) `(3a-5b-c)^(2)`
(iii) `(-x+2y-3z)^(2)`

Explanation

(i) Putting `4a=x,-b=y and 2c =z`, we get
` (4a-b+2c)^2`
`=(x+y+z)^2`
` =x^2+y^2+z^2+2xy+2yz+2zx`
`=(4a)^2+(-b)^2+(2c)^2+{2xx4axx(-b)}+{2xx(-b)xx 2 c }+{2xx 2c xx 4a}`
` =16a^2+b^2+4c^2-8ab-4bc +16ca`.
(ii) Putting `3a=x,-5b=y and -c=z`, we get
`(3a-5b-c)^2`
` =(x+y+z)^2`
` =x^2+y^2+z^2+2xy+2yz+2zx`
`=(3a)^2 +(-5b)^2+(-c)^2+{2xx3axx(-5b)}+{2xx (-5b)xx(-c)}+{2xx(-c)xx3a}`
` =9a^2+25b^2+c^2-30ab+10bc-6ca`.
(iii) Putting `-x=a,2y =b and -3z=c`, we get
`(-x+2y-3x)^2`
` =(a+b+c)^2`
`=a^2+b^2+c^2+2ab+2bc +2ca`
` =(-x)^2+(2y)^2+(-3z)^2+{2xx (-x)xx2y}+{2xx(2y)xx (-3z)} +{2xx(-3z)xx (-x)}`
` =x^2+4y^2+9z^2-4xy-12yz+6xz`.