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

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Question

(A) The given expression is $x^{2}+4 y^{2}+9 z^{2}-4 x y-12 y z+6 z x$.We use the algebraic identity: $(a+b+c)^{2} = a^{2}+b^{2}+c^{2}+2ab+2bc+2ca$.Co

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) The given expression is $x^{2}+4 y^{2}+9 z^{2}-4 x y-12 y z+6 z x$.We use the algebraic identity: $(a+b+c)^{2} = a^{2}+b^{2}+c^{2}+2ab+2bc+2ca$.Comparing the given expression with the identity,we can rewrite it as:$x^{2}+(-2 y)^{2}+(3 z)^{2}+2(x)(-2 y)+2(-2 y)(3 z)+2(3 z)(x)$.Here,$a = x$,$b = -2y$,and $c = 3z$.Thus,the expression simplifies to $(x-2y+3z)^{2}$.Therefore,the factors are $(x-2y+3z)(x-2y+3z)$.

Factorise the expression: $x^{2}+4 y^{2}+9 z^{2}-4 x y-12 y z+6 z x$

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