Factorise x^{3}-8 y^{3}-27-18 x y. | vedclass

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(B) The given expression is $x^{3}-8 y^{3}-27-18 x y$.This can be rewritten as $x^{3} + (-2y)^{3} + (-3)^{3} - 3(x)(-2y)(-3)$.We use the algebraic ide

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$(x-2y-3)(x^2+4y^2+9+2xy-6y+3x)$

Vedclass · Answer

(B) The given expression is $x^{3}-8 y^{3}-27-18 x y$.This can be rewritten as $x^{3} + (-2y)^{3} + (-3)^{3} - 3(x)(-2y)(-3)$.We use the algebraic identity $a^{3} + b^{3} + c^{3} - 3abc = (a+b+c)(a^{2} + b^{2} + c^{2} - ab - bc - ca)$.Here,$a = x$,$b = -2y$,and $c = -3$.Substituting these values into the identity:$= (x - 2y - 3)(x^{2} + (-2y)^{2} + (-3)^{2} - (x)(-2y) - (-2y)(-3) - (-3)(x))$$= (x - 2y - 3)(x^{2} + 4y^{2} + 9 + 2xy - 6y + 3x)$.

Factorise $x^{3}-8 y^{3}-27-18 x y$.

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