Factorise the following expression: 27 x^{3}- | vedclass

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(A) The given expression is $27 x^{3}-8 y^{3}-54 x^{2} y+36 x y^{2}$.This can be rewritten as $(3x)^3 - (2y)^3 - 3(3x)^2(2y) + 3(3x)(2y)^2$.Recall the

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$(3x - 2y)^3$

Vedclass · Answer

(A) The given expression is $27 x^{3}-8 y^{3}-54 x^{2} y+36 x y^{2}$.This can be rewritten as $(3x)^3 - (2y)^3 - 3(3x)^2(2y) + 3(3x)(2y)^2$.Recall the algebraic identity: $(a - b)^3 = a^3 - b^3 - 3a^2b + 3ab^2$.Here,$a = 3x$ and $b = 2y$.Substituting these values into the identity,we get $(3x - 2y)^3$.Thus,the factorised form is $(3x - 2y)(3x - 2y)(3x - 2y)$.

Factorise the following expression: $27 x^{3}-8 y^{3}-54 x^{2} y+36 x y^{2}$

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