Question
Find the following products:
$(1+x)\left(1-x+x^2\right)$
$(1+x)\left(1-x+x^2\right)$
✓
Answer
We have,
$(1+x)\left(1-x+x^2\right)$
$=(1+x)\left[(1)^2-1 \times x+(x)^2\right]$
$=1^3+x^3\left[\because a^3-b^3=(a+b)\left(a^2-a b+b^2\right)\right]$
$\therefore(1+x)\left(1-+x+x^2\right)=1+x^3$
$(1+x)\left(1-x+x^2\right)$
$=(1+x)\left[(1)^2-1 \times x+(x)^2\right]$
$=1^3+x^3\left[\because a^3-b^3=(a+b)\left(a^2-a b+b^2\right)\right]$
$\therefore(1+x)\left(1-+x+x^2\right)=1+x^3$
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