Freaky Factorization!

Factorize $27x^3- 81y^3$ .

Please show your steps and reason wherever needed.

#Algebra

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

$27x^3-81y^3=27(x^3-3y^3)$ 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: $27(x^3-3y^3)=27(x-\sqrt[3]{3}y)(x^2+\sqrt[3]{3}xy+\sqrt[3]{9}y^2)$

Abdur Rehman Zahid - 5 years, 1 month ago

thanks for the help.....

Palaash Barot - 5 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$