# By using binomial theorem, expand $$(1 + x + x^2)^3$$.

## Solution :

Let y = x + $$x^2$$. Then,

$$(1 + x + x^2)^3$$ = $$(1 + y)^3$$

= $$^3C_0$$ + $$^3C_1 y$$ + $$^3C_2 y^2$$ + $$^3C_3 y^3$$

= $$1 + 3y + 3y^2 + y^3$$ = 1 + 3$$(x + x^2)$$ + 3$$(x + x^2)^2$$ + $$(x + x^2)^3$$

= $$x^6 + 3x^5 + 6x^4 + 7x^3 + 6x^2 + 3x + 1$$

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