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Question

Factorise: 2x3+54y3-4x-12y


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Solution

Factorization

The given equation is,

2x3+54y3-4x-12y=2(x3+27y3-2x-6y)

=2{(x3+27y3)2(x+3y)}

We know the identity

a3+b3=(a+b)(a2ab+b2)

2x3+54y3-4x-12y=2{(x+3y)(x2-3xy+9y2)-2(x+3y)}

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

Hence, the result of the factorization of the given expression is 2(x+3y)(x2-3xy+9y2-2).


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