Factorise the following:9 x^{2}+4 y^{2}+16 z^ | vedclass

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(A) We have the expression: $9 x^{2}+4 y^{2}+16 z^{2}+12 x y-16 y z-24 x z$.This can be written in the form $a^{2}+b^{2}+c^{2}+2 a b+2 b c+2 c a = (a+

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$(3x + 2y - 4z)^2$

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(A) We have the expression: $9 x^{2}+4 y^{2}+16 z^{2}+12 x y-16 y z-24 x z$.This can be written in the form $a^{2}+b^{2}+c^{2}+2 a b+2 b c+2 c a = (a+b+c)^{2}$.Here,$a = 3x$,$b = 2y$,and $c = -4z$.Substituting these values:$9 x^{2}+4 y^{2}+16 z^{2}+12 x y-16 y z-24 x z = (3 x)^{2}+(2 y)^{2}+(-4 z)^{2}+2(3 x)(2 y)+2(2 y)(-4 z)+2(-4 z)(3 x)$.Using the identity $(a+b+c)^{2}$,we get:$(3 x+2 y-4 z)^{2}$.Thus,the factorised form is $(3 x+2 y-4 z)(3 x+2 y-4 z)$.

Factorise the following:
$9 x^{2}+4 y^{2}+16 z^{2}+12 x y-16 y z-24 x z$

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Factorise the following:$9 x^{2}+4 y^{2}+16 z^{2}+12 x y-16 y z-24 x z$