\[27x^3-81y^3=27(x^3-3y^3)\]
You can factorize the second factor further by using the algebraic identity \(a^3-b^3=(a-b)(a^2+ab+b^2)\), only there won't be integral coefficients in the resulting factors:
\[27(x^3-3y^3)=27(x-\sqrt[3]{3}y)(x^2+\sqrt[3]{3}xy+\sqrt[3]{9}y^2)\]

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewest\[27x^3-81y^3=27(x^3-3y^3)\] You can factorize the second factor further by using the algebraic identity \(a^3-b^3=(a-b)(a^2+ab+b^2)\), only there won't be integral coefficients in the resulting factors: \[27(x^3-3y^3)=27(x-\sqrt[3]{3}y)(x^2+\sqrt[3]{3}xy+\sqrt[3]{9}y^2)\]

Log in to reply

thanks for the help.....

Log in to reply