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

User UweB
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1 Answer

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\huge \boxed{\mathfrak{Question} \downarrow}

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


\large \boxed{\mathbb{ANSWER \: WITH \: EXPLANATION} \downarrow}


\sf\frac { 8 x ^ { 3 } - 27 y ^ { 3 } } { 2 x - 3 y } \\

Factor the expressions that are not already factored.

How to factorise :-

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


\rightarrow \sf \: (\left(2x-3y\right)\left(4x^(2)+6xy+9y^(2)\right))/(2x-3y) \\

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


\boxed{ \boxed{ \bf \: 4x^(2)+6xy+9y^(2) }}

User Jon Z
by
6.7k points
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