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8x cube minus 27y cube divided by 2x minus 3y

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  • 8x cube minus 27y cube divided by 2x minus 3y.

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[tex] \sf\frac { 8 x ^ { 3 } - 27 y ^ { 3 } } { 2 x - 3 y } \\ [/tex]

Factor the expressions that are not already factored.

How to factorise :-

Rewrite [tex]\sf8x^{3}-27y^{3}[/tex] as [tex]\sf\left(2x\right)^{3}-\left(3y\right)^{3}[/tex]. The difference of cubes can be factored using the algebraic rule: [tex]\sf\:a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right)[/tex].

[tex]\rightarrow \sf \: \frac{\left(2x-3y\right)\left(4x^{2}+6xy+9y^{2}\right)}{2x-3y} \\ [/tex]

Cancel out 2x-3y in both the numerator and denominator.

[tex] \boxed{ \boxed{ \bf \: 4x^{2}+6xy+9y^{2} }}[/tex]

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