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Chapter 5: Problem 41

Combine like terms. Write all answers in descending order. \(7 x^{2}+3 x+4 x^{2}\)

Short Answer

Expert verified
11x^{2} + 3x

Step by step solution

01

Identify Like Terms

The given expression is: \[7x^{2} + 3x + 4x^{2}\]. Identify the like terms. Here, both \(7x^{2}\) and \(4x^{2}\) are like terms because they have the same variable raised to the same power.
02

Combine Like Terms

Add the coefficients of the like terms. The coefficients of \(7x^{2}\) and \(4x^{2}\) are 7 and 4, respectively. Adding them together gives: \[ 7x^{2} + 4x^{2} = (7 + 4)x^{2} = 11x^{2} \].
03

Write the Final Expression

After combining the like terms, write down the simplified expression in descending order: \[11x^{2} + 3x\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

like terms
In algebra, 'like terms' are terms that have identical variables raised to the same powers. For example, in the expression 7x^{2} + 3x + 4x^{2} , the terms 7x^{2} and 4x^{2} are like terms because they both consist of the variable x raised to the power of 2 (making them both x squared terms). To combine like terms, simply add or subtract their coefficients. In this example, 7x^{2} and 4x^{2} can be combined because they share the same variable portion (x^2).
coefficients
Coefficients are the numerical part of the terms that contain variables. In the expression: 7x^{2} + 3x + 4x^{2} , 7, 3, and 4 are the coefficients. They tell you how many times to count the variable portion. When combining like terms, you add the coefficients while keeping the variable portion unchanged. For instance, in: 7x^{2} + 4x^{2} : add the coefficients 7 and 4 to get 11, resulting in 11x^{2} .
descending order
Writing an expression in descending order means arranging the terms from the highest degree to the lowest. The 'degree' of a term is the exponent of the variable in that term. For example, in the expression 11x^{2} + 3x , 11x^{2} is placed before 3x because the exponent 2 (from x^2) is higher than the exponent 1 (from x). Always use descending order when managing polynomial expressions to keep them standardized and easy to read.

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Most popular questions from this chapter

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