Question

Alpha Cube + beta cube is equals to

Answer 1

let me take alpha =x
beta =y
just for convenience
${x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )$

Answer 2

Answer:

$(\alpha+\beta)(\alpha^2 - \alpha.\beta + \beta^2)$

Step-by-step explanation:

Since, we know that,

$(\alpha+\beta)^3=\alpha^3+\beta^3+3.\alpha.\beta(\alpha+\beta)$

$\implies \alpha^3+\beta^3 = (\alpha+\beta)^3 - 3.\alpha.\beta(\alpha+\beta)$

$\implies \alpha^3+\beta^3 = (\alpha + \beta)[(\alpha+\beta)^2-3\alpha.\beta]$

$\implies \alpha^3+\beta^3 = (\alpha + \beta)(\alpha^2+\beta^2+2.\alpha.\beta-3.\alpha.\beta)$

( Because, (a+b)² = a² + 2ab + b² ),

$\implies \alpha^3+\beta^3 = (\alpha + \beta)(\alpha^2+\beta^2-\alpha.\beta)$

Which is the required answer.