Question
Find the following product:
$\left(x^2-1\right)\left(x^4+x^2+1\right)$
$\left(x^2-1\right)\left(x^4+x^2+1\right)$
✓
Answer
$\left(x^2-1\right)\left(x^4+x^2+1\right)$
$=\left(x^2-1\right)\left\{\left(x^2\right)^2+\left(x^2\right)(1)+(1)^2\right\}$
$=\left(x^2\right)^3-(1)^3$
${\left[\therefore(a+b)\left(a^2-a b+b^2\right)=a^3+b^3\right]}$
$=x^6-1$
$=\left(x^2-1\right)\left\{\left(x^2\right)^2+\left(x^2\right)(1)+(1)^2\right\}$
$=\left(x^2\right)^3-(1)^3$
${\left[\therefore(a+b)\left(a^2-a b+b^2\right)=a^3+b^3\right]}$
$=x^6-1$
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