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Chapter 5: Problem 10

Add or subtract as indicated. $$\left(-2 x^{2} y+x y\right)+\left(4 x^{2} y+7 x y\right)$$

Short Answer

Expert verified
The solution is \(2 x^{2} y + 8 x y\).

Step by step solution

01

Identify like terms

In each of the parentheses we have two terms. In the first, we have \(-2 x^{2} y\) and \(x y\); in the second, we have \(4 x^{2} y\) and \(7 x y\). We see that \(-2 x^{2} y\) and \(4 x^{2} y\) are alike as they both contain variables \(x\) and \(y\) and the power of each variable is the same (2 for \(x\) and 1 for \(y\)). Similarly, \(x y\) and \(7 x y\) are alike.
02

Add like terms together

We add the like terms \(-2 x^{2} y\) and \(4 x^{2} y\) together to get \(2 x^{2} y\). Then we add \(x y\) and \(7 x y\) together. Since there鈥檚 no specified number in front of \(x y\), we can assume it鈥檚 1, so \(1 x y + 7 x y = 8 x y\).
03

Write out the final solution

After adding the like terms, the final solution is \(2 x^{2} y + 8 x y\).

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