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Question

Verify:
(i) x3+y3=(x+y)(x2xy+y2)
(ii) x3y3=(xy)(x2+xy+y2)


Solution

(i) Given x3+y3=(x+y)(x2xy+y2)

R.H.S : (x+y)(x2xy+y2)=x(x2xy+y2)+y(x2xy+y2)

=x3x2y+xy2+yx2xy2+y3=x3+y3 
Grouping the like terms, we get
=x3x2y+x2y+xy2xy2+y3
=x3+y3      (Cancel opposite signs terms)
which is equal to L.H.S

(ii) x3y3=(xy)(x2+xy+y2)

 R.H.S : (xy)(x2+xy+y2)=x(x2+xy+y2)y(x2+xy+y2)

=x3+x2y+xy2yx2xy2y3
Grouping the like terms, we get 
=x3+x2yx2y+xy2xy2y3   
=x3y3   (Cancel opposite signs terms)
 which is equal to L.H.S


Mathematics

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