Question

Simplify:

\[\frac{8 x^3 - 27 y^3}{4 x^2 - 9 y^2}\]

Answer 1

It is known that,

a² − b² = (a + b) (a − b)

a³ − b³ = (a − b)(a² + ab + b²)

\[\  \frac{8 x^3 - 27 y^3}{4 x^2 - 9 y^2}\]

\[ = \frac{\left( 2x \right)^3 - \left( 3y \right)^3}{\left( 2x \right)^2 - \left( 3y \right)^2}\]

\[ = \frac{\left( 2x - 3y \right)\left[ \left( 2x \right)^2 + \left( 2x \right) \times \left( 3y \right) + \left( 3y \right)^2 \right]}{\left( 2x + 3y \right)\left( 2x - 3y \right)}\]

\[= \frac{\left(2x - 3y \right)\left(4 x^2 + 6xy + 9 y^2 \right)}{\left( 2x + 3y \right)\left(2x - 3y \right)}\]

\[= \frac{4 x^2 + 6xy + 9 y^2}{\left(2x + 3y \right)}\]