Question
Factorize the following expressions:
$a^3 + b^3 + a + b$
$a^3 + b^3 + a + b$
✓
Answer
$a^3 + b^3 + a + b$
$= (a^3 + b^3) + 1(a + b)$
$= (a + b)(a^2 - ab + b^2) + 1(a + b)$
$\big[\therefore$ $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$$\big]$
$= (a + b)(a^2 - ab + b^2 + 1)$
$\therefore$ $a^3 + b^3 + a + b = (a + b)(a^2 - ab + b^2 + 1)$
$= (a^3 + b^3) + 1(a + b)$
$= (a + b)(a^2 - ab + b^2) + 1(a + b)$
$\big[\therefore$ $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$$\big]$
$= (a + b)(a^2 - ab + b^2 + 1)$
$\therefore$ $a^3 + b^3 + a + b = (a + b)(a^2 - ab + b^2 + 1)$
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