Question
Factorize the following expressions:
$a^3 + 3a^2b + 3ab^2 + b^3 - 8$
$a^3 + 3a^2b + 3ab^2 + b^3 - 8$
✓
Answer
$= (a + b)^3 - 8$
$\big[\therefore$ $a^3 + 3a^2b + 3ab^2 + b^3 = (a + b)$3$\big]$
$= (a + b)^3 - 23$
$= (a + b - 2)((a + b)^2 + (a + b) \times 2 + 2^2)$
$= (a + b - 2)(a² + 2ab + b² + 2a + 2b + 4)$
$\therefore$ $a^3 + 3a^2b + 3ab^2 + b^3 - 8$
$= (a + b - 2)(a² + 2ab + b² + 2a + 2b + 4)$
$\big[\therefore$ $a^3 + 3a^2b + 3ab^2 + b^3 = (a + b)$3$\big]$
$= (a + b)^3 - 23$
$= (a + b - 2)((a + b)^2 + (a + b) \times 2 + 2^2)$
$= (a + b - 2)(a² + 2ab + b² + 2a + 2b + 4)$
$\therefore$ $a^3 + 3a^2b + 3ab^2 + b^3 - 8$
$= (a + b - 2)(a² + 2ab + b² + 2a + 2b + 4)$
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