Question
Factorise $: 2x^3+ 54y^3- 4x - 12y$
✓
Answer
$2x^3+ 54y^3- 4x - 12y$
$= 2 ( x^3+ 27y^3 - 2x - 6y )$
$= 2 [ { (x)^3+ (3y)^3}- 2(x+ 3y) ]$
$[$ Using identity $(a^3+b^3) = (a + b)(a^2-ab+ b^2) ]$
$= 2[ {(x + 3y)(x^2- 3xy + 9y^2)} - 2(x + 3y) ]$
$= 2(x + 3y)(x^2- 3xy + 9y^2- 2)$
$= 2 ( x^3+ 27y^3 - 2x - 6y )$
$= 2 [ { (x)^3+ (3y)^3}- 2(x+ 3y) ]$
$[$ Using identity $(a^3+b^3) = (a + b)(a^2-ab+ b^2) ]$
$= 2[ {(x + 3y)(x^2- 3xy + 9y^2)} - 2(x + 3y) ]$
$= 2(x + 3y)(x^2- 3xy + 9y^2- 2)$
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