1.

Find the total number of terms in (1+x+x^2)^3.

Answer»

Solution :`(1+x)^2=1+x^2+2x`
`(1+x)^3=1+3x+3x^2+x^3`
`(1+x)^4=1+4x+6x^2+4x^3+x^4`
`(1+x+x^2)^2=1+2x+3x^2+2x^3+x^4`
`(1+x+x^2)^3=1+3x+6x^2+7x^3+6x^4+3x^5+x^6`
This shows that total NUMBER of TERMS in
`(1+x+x^2+….x^n)^m=(m.n)+1`


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