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Question

Verify (x3-y3)=(x-y)(x2+xy+y2)using some non-zero positive integers and check by actual multiplication.


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Solution

Step 1: Verify (x3-y3)=(x-y)(x2+xy+y2)by actual multiplication.

Let us expand R.H.S.

(x-y)(x2+xy+y2)=x3-x2y+x2y–xy2+xy2–y3=x3–y3=LHS

Hence Proved.

Step 2: Substituting some non-zero positive integers and check by actual multiplication.

Put x=3,y=2

L.H.S.=x3–y3=33–23=27–8=19

R.H.S.=(x-y)(x2+xy+y2)=(3-2)(32+6+22)=9+6+4=19

R.H.S.=L.H.S.

Hence proved.


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