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Question
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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