Question

factors of 27x3 -1/x3​

Answer 1

$\pink{ \boxed{Answer}}$

(3x - 1/x)(9x² + 3 +1/x²)

$\pink{ \boxed{step \: by \: step \: explanation}}$

$27 {x}^{3} - { \frac{1}{x ^{3} }} \\ \\ = ( {3x})^{3} - ({ \frac{1}{x} })^{3} \\ \\ = (3x - \frac{1}{x} )[ ({3x)}^{2} + 3x \times \frac{1}{x} + { (\frac{1}{x} })^{2}] \\ \\ = (3x - \frac{1}{x} )(9 {x}^{2} + 3 + \frac{1}{ {x}^{2} } )$

$\pink{\boxed{Formula \: used}}$

• x³ - y³ = (x - y)( x² + xy +y²)

Answer 2

Step-by-step explanation:

Given:

• 27x³ – 1/x³

$27x {3} - \frac{1}{ {x}^{3} }$

$(3x) ^{3} - \: ( \frac{1}{x} ) ^{3}$

$we \: know \: that \: {a}^{3} - {b}^{3} = (a \: - b) {a}^{2} + {b}^{2} + 2ab$

$(3x - \frac{1}{x} )(3x )^{2} + ( \frac{1}{x}) ^{2} + 3x \times \frac{1}{x}$

→ (3x – 1/x) (9x² + 1/x² + 3)