Question

find the ratio of
a^3 + b^3 and a^2 - b^2​

Answer 1

Formulae:

a³ + b³ = (a + b) (a² - ab + b²)

a² - b² = (a + b) (a - b)

Now,

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

Therefore,

(a³ + b³) : (a² - b²) = (a² - ab + b²) : (a - b)