Question
Factorize the following expressions:
x6 + y6
x6 + y6
✓
Answer
= (x2)3 + (y2)3
= (x2 + y2)((x2)2 - x2y2 + (y2)2)
= (x2 + y2)(x4 - x2y2 + y4)
$\big[\therefore$ a3 + b3 = (a + b)(a2 - ab + b2)$\big]$
$\therefore$ x6 + y6 = (x2 + y2)(x4 - x2y2 + y4)
= (x2 + y2)((x2)2 - x2y2 + (y2)2)
= (x2 + y2)(x4 - x2y2 + y4)
$\big[\therefore$ a3 + b3 = (a + b)(a2 - ab + b2)$\big]$
$\therefore$ x6 + y6 = (x2 + y2)(x4 - x2y2 + y4)
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