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 \: (\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) }}`