Question

Factorise the following :
`(i) 9x^(2)+4y^(2)+16z^(2)+12xy-16yz-24xz`
`(ii) 25x^(2)+16y^(2)+4z^(2)-40xy +16yz-20 xz`
`(iii) 16x^(2)+4y^(2)+9z^(2)-16xy-12yz+24xz`

Answer 1

We observe here that `-40xy and -20 xz` are negative terms in the given expression and x occurs in both the terms.
So, we write , `25x^2 "as" (-5x)^2`.
` therefore 25x^2+16y^2+4z^2-40xy+16yz-20xz`
` =(-5z)^2+(4y)+(2z)^2+{2xx (-5x)xx (4y)}+{2xx (4y)xx (2z)}+{2xx (-5x)xx (2z)}`
` ={(-5x)+4y+2z)}^2=(-5x+4y+2z)^2`.