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Chapter 5: Problem 12

Add or subtract as indicated. $$\left(7 x^{2} y+5 x y+13\right)+\left(-3 x^{2} y+6 x y+4\right)$$

Short Answer

Expert verified
The solution is \(4 x^{2} y + 11xy + 17\).

Step by step solution

01

Identify Like Terms

From the expression, the like terms are \(7 x^{2} y\) and \(-3 x^{2} y\) (both have variables \(x^{2}y\)), \(5xy\) and \(6xy\) (both have a single \(x\) and \(y\)), and the constants \(13\) and \(4\).
02

Addition of Like Terms

Add the coefficients of the like terms and preserve the common variables with their respective powers. Addition of \(7 x^{2} y\) and \(-3 x^{2} y\) results in \(4 x^{2} y\). Similarly, \(5xy\) and \(6xy\) result in \(11xy\), and \(13 + 4\) gives \(17\).
03

Combine All Terms

Combine all the terms obtained from Step 2. They form the simplified sum of the given expression.

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Explain how to divide a polynomial that is not a monomial by a monomial. Give an example.

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