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5.Factorize :
i)\(4x^2 + 9y^2 + 16z^2 + 12xy - 24yz - 16xz\)
ii)\(2x^2 + y^2 + 8z^2 - 2\sqrt{2}xy + 4\sqrt{2}yz - 8xz\)
Answer :

i)\(4x^2 + 9y^2 + 16z^2 + 12xy - 24yz - 16xz \)
\(= (2x)^2 + (3y)^2 - (4z)^2 + 2(2x)(3y) - 2(3y)(4z) - 2(2x)(4z)\)
\(=(2x + 3y - 4z)^2\)

ii)\(2x^2 + y^2 + 8z^2 - 2\sqrt{2}xy + 4\sqrt{2}yz - 8xz \)
= \(-\sqrt{2}x)^2 + (y)^2 + (2\sqrt{2}z)^2 - 2(\sqrt{2}x)(y) + 2(y)(2\sqrt{2}z) - 2(\sqrt{2}x)(2\sqrt{2}z)\)
\(=(-\sqrt{2}x + y + 2\sqrt{2}z)^2\)