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Algebraic Expressions and Identities — MATHS STD 8 — Question

Gujarat 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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