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Chapter 4: Problem 29

If the terms are like terms, add them. If they are unlike terms, state unlike terms. $$15 x^{4} y^{2},-9 x^{4} y^{2}, 4 x^{4} y^{2}$$

Short Answer

Expert verified
The addition of the given terms is \(10 x^{4} y^{2}\).

Step by step solution

01

Identify Like Terms

First, identify if the terms are 'like terms' or 'unlike terms'. 'Like Terms' are those which have exactly the same variables and powers. Looking at the terms \(15 x^{4} y^{2}\), \(-9 x^{4} y^{2}\), and \(4 x^{4} y^{2}\), you can see they are 'like terms' because all of them have the same variables \(x\) and \(y\) with the same powers 4 and 2 respectively.
02

Add or Subtract Coefficients

Next, add or subtract the coefficients of these like terms individually. In this case, add the coefficients 15, -9 and 4.
03

Write the Final Answer

Write the final answer by combining the result from step 2 with the common variable part. The coefficients add up to 10, so the final answer is \(10 x^{4} y^{2}\).

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