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Question 5: Factorize x 3 + 3 x y 2 – 2 x 2 y – 6y 3

Question 5: Factorize   x^{3}+3xy ^{2}-2x ^{2}y-6y ^{3}

a square minus b square type expressions

Solution:

The given expression is

 x^{3}+3xy ^{2}-2x ^{2}y-6y ^{3}

Re-arranging expression as;

=  x^{3}-2x ^{2}y+3xy ^{2}-6y ^{3}

Taking out  x^{2 } and 3 y^{2 } as common from two first and two last terms respectively;

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

Put brackets as under;

 =[x^{2 }(x-2y) + 3y ^{2}(x-2y)]

Now we can see (x-2y) as common – take it out;

 =(x-2y)[x^{2 } + 3y ^{2}]

so,

 x^{3}+3xy ^{2}-2x ^{2}y-6y ^{3}  =(x-2y)(x^{2 } + 3y ^{2})

 

 

 


 

 

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