Maharashtra BoardEnglish MediumSTD 9MathsAlgebraic Identities2 Marks
Question
Find the following:
$\left(x^3+1\right)\left(x^6-x^3+1\right)$
✓
Answer
We have,
$\left(x^3+1\right)\left(x^6-x^3+1\right)$
$=\left(x^3+1\right)\left[\left(x^3\right)^2-1 x x^3+1^2\right]$
$=\left(x^3\right)^3+(1)^3\left[\because a^3+b^3=(a+b)\left(a^2-a b+b^2\right)\right]=x^9+1$
$\therefore\left(x^3+1\right)\left(x^6-x^3+1\right)=x^9+1$
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