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Chapter 5: Problem 83

See the Concept Checks in this section. $$5 a+6 a$$

Short Answer

Expert verified
The solution is \(11a\).

Step by step solution

01

Understand Like Terms

Like terms in an expression are those with the same variable and exponent. In the expression given, both terms, \(5a\) and \(6a\), have the same variable \(a\). Hence, they are like terms that can be combined together.
02

Combine Like Terms

To combine like terms, simply add or subtract their coefficients. Here, the coefficients are \(5\) and \(6\). Therefore, calculate \(5 + 6\) to combine the terms.
03

Calculate the Result

Add the coefficients \(5 + 6 = 11\). So, combining the terms results in \(11a\).

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Key Concepts

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

Like Terms
In algebra, understanding the concept of like terms is crucial for simplifying expressions. Like terms are terms within an expression that have identical variable parts. This means the variables and their exponents are exactly the same. For example, in the expression \(5a + 6a\), both terms contain the variable \(a\), meaning they are like terms. Recognizing like terms allows us to combine them, simplifying the expression into a more manageable form. Other examples of like terms include \(3x\) and \(7x\), or \(2y^2\) and \(-4y^2\). The variables are the same, and so are the exponents, making them combinable.
Coefficients
Coefficients are the numerical part of terms in an algebraic expression. They usually follow a variable or a set of variables. In other words, they are the numbers that multiply the variables in a term. Taking the expression \(5a + 6a\), we see the coefficients are \(5\) and \(6\). When it comes to combining like terms, we focus on these coefficients. You add or subtract the coefficients to combine the terms efficiently. When performing calculations like adding \(5a + 6a\), you add the coefficients \(5 + 6\), yielding \(11a\).
Understanding coefficients is vital because it allows us to simplify expressions and solve equations more effectively.
Algebraic Expressions
Algebraic expressions are mathematical statements that include numbers, variables, and operations. They do not include an equal sign like equations do. Expressions like \(5a + 6a\) are simple, yet they serve as the foundation for more complex algebra problems. In an expression, terms are separated by addition or subtraction. Each term can be a constant or a variable multiplied by a coefficient. For example, in \(5a + 6a\), \(5a\) and \(6a\) are the terms.
  • Terms are parts of the expression separated by \(+\) or \(-\).
  • Constants have no variables attached, like the number \(3\) in an expression \(x + 3\).
  • Expressions can be simplified by combining like terms, making them easier to work with.
By understanding algebraic expressions, students are better equipped to tackle more advanced topics in algebra.

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Most popular questions from this chapter

Divide. $$ \frac{x^{5}+x^{2}}{x^{2}+x} $$

Simplify. $$ \left(2 a^{3}\right)^{3} a^{4}+a^{5} a^{8} $$

Simplify. $$ \left(2 a^{3}\right)^{3} a^{-3}+a^{11} a^{-5} $$

Multiply each expression. $$ 2 x\left(x^{2}+7 x-5\right) $$

Simplify each polynomial by combining like terms. $$ 7.75 x+9.16 x^{2}-1.27-14.58 x^{2}-18.34 $$
See all solutions

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