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Algebraic Expressions and Identities — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsAlgebraic Expressions and Identities2 Marks
Question
Multiply:
$\big(−\frac{\text{a}}{7}+\frac{\text{a}^2}{9}) \ \text{by}\big(\frac{\text{b}}{2}−\frac{\text{b}^2}{3}\big)$
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Answer

To multiply, we will use distributive law as follows:$\big(−\frac{\text{a}}{7}+\frac{\text{a}^2}{9}) \ \text{by}\big(\frac{\text{b}}{2}−\frac{\text{b}^2}{3}\big)$
$=\big(−\frac{\text{a}}{7}\big)\big(\frac{\text{b}}{2}−\frac{\text{b}^2}{3}\big)+\big(\frac{\text{a}^2}{9}\big)\big(\frac{\text{b}}{2}−\frac{\text{b}^2}{3}\big)​​​​​​​$
$=(−\frac{\text{ab}}{14}+\frac{ab^2}{21}\big)+\big(\frac{\text{a}^2\text{b}}{18}−\frac{\text{a}^2\text{b}^2}{27}\big)$
$=−\frac{\text{ab}}{14}+\frac{\text{ab}^2}{21}+\frac{\text{a}^2\text{b}}{18}−\frac{\text{a}^2\text{b}^2}{27}$
Thus, the answer is $−\frac{\text{ab}}{14}+\frac{\text{ab}^2}{21}+\frac{\text{a}^2\text{b}}{18}−\frac{\text{a}^2\text{b}^2}{27}.$

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