Question
Factorize:
a3x3 - 3a2bx2 + 3ab2x - b3
a3x3 - 3a2bx2 + 3ab2x - b3
✓
Answer
a3x3 - 3a2bx2 + 3ab2x - b3
= (ax)3 - 3(ax)2 × b + 3(ax)b2 - b3
= (ax - b)3 $\big[\because$ a3 - 3a2b + 3ab2 - b3= (a - b)3$\big]$
= (ax - b)(ax - b)(ax - b)
$\therefore$ a3x3 - 3a2bx2 + 3ab2x - b3
= (ax - b)(ax - b)(ax - b)
= (ax)3 - 3(ax)2 × b + 3(ax)b2 - b3
= (ax - b)3 $\big[\because$ a3 - 3a2b + 3ab2 - b3= (a - b)3$\big]$
= (ax - b)(ax - b)(ax - b)
$\therefore$ a3x3 - 3a2bx2 + 3ab2x - b3
= (ax - b)(ax - b)(ax - b)
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Factorize:
a2 + b2 + 2(ab + bc + ca)
a2 + b2 + 2(ab + bc + ca)