Factorise each of the following: 8 $a^{3}$ – $b^{3}$ – 12 $a^{2}$ b + 6a $b^{2}$

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Solution

8 $a^{3}$ – $b^{3}$ – 12 $a^{2}$ b + 6a $b^{2}$

= ${(2 a)}^{3}$ - $b^{3}$ - 3 ${(2 a)}^{2}$ b + 3(2a) $b^{2}$

∵ ${(x - y)}^{3}$ = $x^{3}$ - $y^{3}$ - 3xy(x - y) = $x^{3}$ - 3 $x^{2}$ y + 3x $y^{2}$ - $y^{3}$

= ${(2 a - b)}^{3}$

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