. Factorise: (i) 4x2 + !Ji' + 16z2 + 12xy - 24yz - 16zz (U) 2il + y2 + 8z2 -_ 2./2 xy + 4 ./2yz - Bzz.

(i) 4x2 + 9y2 + 1&2 + 12.xy - 24yz - 16.u = (2x'f + (3y)2 + <- 4z>2+ 2(2xX3y) + 2(3yX- 4z) + 2(2x)(- 4z) [Using identity::r2 + y2 + z2 + 2xy + 2yz + 2a = (% + y + z)2J = (2x + Sy - 4z>2. = (2x + 3y - 4z)(2x + 3y - 4.z). (ii) 2x2 + y2 + sz2 - 2 J2 xy + 4 J2yz - 8xz = (- J2,s'f + ( y'f + (2./2z'f + 2(- .J2x)( y) + 2(y)(2J2z) + 2(- .J2xX2J2z) [Using identity: :r2 + i' + z2 + 2xy + 2yz + 2.u = (% + y + z = (- Ji x + y + 2J2 z'f = (- .J2z + y + 2./2 zX- .J2x + y + 2./2 z).