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Add the Following Algebraic Expression: 7 2 X 3 − 1 2 X 2 + 5 3 , 3 2 X 3 + 7 4 X 2 − X + 1 3 , 3 2 X 2 − 5 2 X − 2 - Mathematics

Answer in Brief

Add the following algebraic expression: \[\frac{7}{2} x^3 - \frac{1}{2} x^2 + \frac{5}{3}, \frac{3}{2} x^3 + \frac{7}{4} x^2 - x + \frac{1}{3}, \frac{3}{2} x^2 - \frac{5}{2}x - 2\]

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Solution

To add, we proceed as follows:

\[\left( \frac{7}{2} x^3 - \frac{1}{2} x^2 + \frac{5}{3} \right) + \left( \frac{3}{2} x^3 + \frac{7}{4} x^2 - x + \frac{1}{3} \right) + \left( \frac{3}{2} x^2 - \frac{5}{2}x - 2 \right)\]

\[ = \frac{7}{2} x^3 - \frac{1}{2} x^2 + \frac{5}{3} + \frac{3}{2} x^3 + \frac{7}{4} x^2 - x + \frac{1}{3} + \frac{3}{2} x^2 - \frac{5}{2}x - 2\]

\[ = \frac{7}{2} x^3 + \frac{3}{2} x^3 - \frac{1}{2} x^2 + \frac{7}{4} x^2 + \frac{3}{2} x^2 - x - \frac{5}{2}x + \frac{5}{3} + \frac{1}{3} - 2 ( \text { Collecting like terms })\]

\[ = 5 x^3 + \frac{11}{4} x^2 - \frac{7}{2}x ( \text { Combining like terms })\]

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APPEARS IN

RD Sharma Class 8 Maths
Chapter 6 Algebraic Expressions and Identities
Exercise 6.2 | Q 1.6 | Page 5
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