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

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

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

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