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Chapter 10: Problem 32

Use a vertical format to add or subtract. $$\left(2 m-8 m^{2}-3\right)+\left(m^{2}+5 m\right)$$

Short Answer

Expert verified
-7m^2 + 7m - 3

Step by step solution

01

Arrange in vertical format

This requires grouping and aligning like terms from both polynomials. Group the terms such that the terms with \(m^2\) are on top, followed by the terms with \(m\), then the constant. We have: \[\begin{array}{c} 2m \ -8m^{2} \ -3 \\ +\ m^{2} \ +5m \ \end{array}\]
02

Add or subtract

Here, it's clear that negative \(-8m^2\) and positive \(m^2\) are like terms and can be added together. Similarly, \(2m\) and \(5m\) are like terms and can be added together. So, the sum becomes \[-8m^2 + m^2 = -7m^2\] and \[2m + 5m = 7m\] Lastly, the constant, \(-3\) doesn't have a like term to be added to, so it remains as it is.
03

Express the final answer

Combine all the results obtained in step 2 to get the final answer which will be: \[-7m^2 + 7m - 3\]

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