Question

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

Answer 1

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

• 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: $\sf\:a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right)$.

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

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

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