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