Find the following products:$ (1+x)\left(1-x+x^{2}\right) $

Given: 

\( (1+x)\left(1-x+x^{2}\right) \)

To do: 

We have to find the given product.

Solution: 

We know that,

$a^{3}+b^{3}=(a+b)(a^{2}-a b+b^{2})$

$a^{3}-b^{3}=(a-b)(a^{2}+a b+b^{2})$

Therefore,

$(1+x)(1-x+x^{2})=(1+x)[(1)^{2}-1 \times x+(x)^{2}]$

$=(1)^{3}+(x)^{3}$

$=1+x^{3}$

 Hence, $(1+x)(1-x+x^{2})=1+x^{3}$. 

Tutorialspoint

Updated on: 10-Oct-2022

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