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Algebraic Expressions and Identities — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsAlgebraic Expressions and Identities3 Marks
Question
Take away:
$\frac{5\text{a}^2}{2}+\frac{3\text{a}^3}{2}+\frac{\text{a}}{3}−\frac{6}{5}$ from $\frac{1}{3}\text{a}^3−\frac{3}{4}\text{a}^2−\frac{5}{2}$
✓

Answer

The difference is given by:$\big(\frac{1}{3}\text{a}^3−\frac{3}{4}\text{a}^2−\frac{5}{2}\big)-\\\big(\frac{5\text{a}^2}{2}+\frac{3\text{a}^3}{2}+\frac{\text{a}}{3}−\frac{6}{5}\big)$
$=\frac{1}{3}\text{a}^3−\frac{3}{4}\text{a}^2−\frac{5}{2}-\frac{5\text{a}^2}{2}\\-\frac{3\text{a}^3}{2}-\frac{\text{a}}{3}+\frac{6}{5}$
$=\frac{1}{3}\text{a}^3−\frac{3\text{a}^{3}}2−\frac{3\text{a}^2}{4}-\frac{5\text{a}^{2}}{2}−\frac{\text{a}}{3}\\−\frac{5}{2}+\frac{6}{5} $
$=\big(\frac{2−9}{6}\big)\text{a}^3+\big(\frac{−3−10}{4})\text{a}^2\\−\frac{\text{a}}{3}+\big(\frac{−25+12}{10}\big)$ (Collecting like terms)
$=-\frac{7}{6}\text{a}^3-\frac{13}{4}\text{a}^2-\frac{\text{a}}{3}-\frac{13}{10 } $ (Combining like terms)

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