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Chapter 5: Problem 9

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

Short Answer

Expert verified
The simplified expression is \(7 x^{2} y - 4 x y\).

Step by step solution

01

Identify like terms

First, identify the like terms in the polynomials, which are terms with the same variable(s) and exponent(s). In this case, the like terms are \(5 x^{2} y\) with \(2 x^{2} y\) and \(-3 x y\) with \(-x y\).
02

Add/Subtract like terms

Next, add or subtract the like terms (coefficients are added or subtracted, while variables remain the same). So, \(5 x^{2} y + 2 x^{2} y\) = \(7 x^{2} y\) and \(-3 x y - x y\) = \(-4 x y\).
03

Write the final simplified expression

Lastly, combine the results from step 2 to get the final simplified expression of the polynomials. So the final answer is \(7 x^{2} y - 4 x y\).

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Most popular questions from this chapter

Simplify: \(24+8 \cdot 3+28 \div(-7)\).

Use a vertical format to find each product. $$\begin{aligned}&4 z^{3}-2 z^{2}+5 z-4\\\&3 z-2\end{aligned}$$

What polynomial, when divided by \(3 x^{2}\), yields the trinomial \(6 x^{6}-9 x^{4}+12 x^{2}\) as a quotient?

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. If \(5^{-2}\) is raised to the third power, the result is a number between 0 and 1

Use a vertical format to find each product. $$\begin{array}{r}7 x^{3}-5 x^{2}+6 x \\\3 x^{2}-4 x \\\\\hline\end{array}$$
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