1.

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

Answer» (i) `9x^(2)+4y^(2)+16z^(2)+12xy-16yz-24xz`
`=(3x)^(2)+(2y)^(2)+(-4z)^(2)+2(3x)(2y((-4z)+2(-4z)(3x)`
[using identity ,`(a+b+c)^(2)=a^(2)+b^(2)+c^(2)+2ab+2bc+ca`]
(ii) `25x^(2)+16y^(2)+4z^(2)-40xy+16yz-20xz`
`=(-5)^(2) +(4y)^(2) +(2z)^(2)(-5x)(4y)+2(4y)(2z)+(22z)(-5x)`
[using identiity ,`(a+b+c)^(2)=a^(2)+b^(2)+c^(2)+2ab+2bc+2ca]`
`16x^(2)+4y^(2)+9z^(2)-16xy-12yz+24xz`
[using identity,`(a+b+c)^(2)=a^(2)+b^(2)+c^(2)+2ab+2bc+2ca`]
`=(4x-2y+3z)^(2)=(4x-2y+3z)(4x-2y+3z)`


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