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CBSE Class 9 Mathematics Question 23 of 30

Polynomials — Question 9

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9
Question

Question 9

Verify :

(i) x3 + y3 = (x + y) (x2 - xy + y2)

(ii) x3 - y3 = (x - y) (x2 + xy + y2)

Answer

(i) x3 + y3 = (x + y) (x2 - xy + y2)

R.H.S

= (x + y) (x2 - xy + y2)

= (x)(x2 - xy + y2) + (y)(x2 - xy + y2)

= x3 - x2y + xy2 + yx2 - xy2 + y3

= x3 + y3

Hence, L.H.S = R.H.S

(ii) x3 - y3 = (x - y) (x2 + xy + y2)

R.H.S

= (x - y) (x2 + xy + y2)

= (x)(x2 + xy + y2) - (y)(x2 + xy + y2)

= x3 + x2y + xy2 - yx2 - xy2 - y3

= x3 - y3

Hence, L.H.S = R.H.S