Factorise 27 x^{3}-y^{3}+64 z^{3}+36 x y z. | vedclass

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Question

(A) We use the algebraic identity: $a^{3}+b^{3}+c^{3}-3 a b c = (a+b+c)(a^{2}+b^{2}+c^{2}-a b-b c-c a)$.Given expression: $27 x^{3}-y^{3}+64 z^{3}+36

Vedclass · Accepted Answer

$(3 x-y+4 z)(9 x^{2}+y^{2}+16 z^{2}+3 x y+4 y z-12 z x)$

Vedclass · Answer

(A) We use the algebraic identity: $a^{3}+b^{3}+c^{3}-3 a b c = (a+b+c)(a^{2}+b^{2}+c^{2}-a b-b c-c a)$.Given expression: $27 x^{3}-y^{3}+64 z^{3}+36 x y z = (3 x)^{3}+(-y)^{3}+(4 z)^{3}-3(3 x)(-y)(4 z)$.Here,$a = 3 x$,$b = -y$,and $c = 4 z$.Substituting these values into the identity:$= (3 x-y+4 z)((3 x)^{2}+(-y)^{2}+(4 z)^{2}-(3 x)(-y)-(-y)(4 z)-(4 z)(3 x))$.$= (3 x-y+4 z)(9 x^{2}+y^{2}+16 z^{2}+3 x y+4 y z-12 z x)$.

Factorise $27 x^{3}-y^{3}+64 z^{3}+36 x y z$.

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