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Algebraic Expressions and Identities — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsAlgebraic Expressions and Identities2 Marks
Question
Simplify:
$a^2 b\left(a^3-a+1\right)-a b\left(a^4-2 a^2+2 a\right)-b\left(a^3-a^2-1\right)$
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Answer

To simplify, we will use distributive law as follows:
$a^2 b\left(a^3-a+1\right)-a b\left(a^4-2 a^2+2 a\right)-b\left(a^3-a^2-1\right)$
$=a^5 b-a^3 b+a^2 b-a^5 b+2 a^3 b-2 a^2 b-a^3 b+a^2 b+b$
$=a^5 b-a^5 b-a^3 b+2 a^3 b-a^3 b+a^2 b-2 a^2 b+a^2 b+b$
$=b$

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