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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, $(1+x)(1-x+x^{2})=1+x^{3}$.
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