Question

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 1

(i) We have , `9x^(2)+4y^(2)+16z^(2)+12xy-16yz-24xz`
`=(3x)^(2)+(2y)^(2)+(-4z)^(2)+2(3x)(2y)+2(2y)(-4z)+2(-4z)(3x)`
`={3x+2y+(-4z)}^(2) [because a^(2)+b^(2)+c^(2)+2ab+2bc+2ca=(a+b+c)^(2)]`
`=(3x+2y-4z)^(2)=(3x+2y-4z)(3x+2y-4z)`
(ii) We have, `25x^(2)+16y^(2)+4z^(2)-40xy+16yz-20xz`
`=(-5x)^(2)+(4y)^(2)+(2z)^(2)+2(-5)(4y)+2(4y)(2z)+2(2z)(-5x)`
`=(-5x+4y+2z)^(2)`
(iii) We have , `16x^(2)+4y^(2)+9z^(2)-16xy-12yz+24xz`
`=(4x)^(2)+(-2y)^(2)+(3z)^(2)+2(4x)(-2y)+2(-2y)(3z)+2(3z)(4x)`
`{4x+(-2y)+3z}^(2) [because a^(2)+b^(2)+c^(2)+2ab+2bc+2ca=(a+b+c)^(2)]`
`=(4x-2y+3z)^(2)`
=(4x-2y+3z)(4x-2y+3z)