Factorise 2x^3+54y^3-4x-12y

Given equation

2x3+54y3-4x-12y

We need to factorize it

Solution

Taking out 2 as a common factor and arranging the like terms we get

2 (x3 – 2x + 27y3 – 6y)

2(x3 + 27y3) – 4(x + 3y)

We know the identity

a3 + b3= (a + b) (a2 – ab + b2)

So will solve the bracket (x3 + 27y3) based in the above identity

= 2(x + 3y) (x2 – 3xy + 9y2) – 4(x + 3y)

(x + 3y)can be taken put as a common factor

= (x + 3y) [2(x2 – 3xy + 9y2) – 4]

= 2(x + 3y) [(x2 – 3xy + 9y2) – 4]

= 2(x + 3y) (x2 – 3xy + 9y2 – 4)

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