Problem 41 Simplify. $$-18 a-3 a$$... [FREE SOLUTION]

91影视

Beginning Algebra: A Guided Approach

Rosemary Karr, Marilyn Massey, R. David Gustafson

$Math Studyset 91影视 Explanations$ Math

10 Edition

Chapter 4: Problem 41

Simplify. $$-18 a-3 a$$

Short Answer

Expert verified

$-21a$

Step by step solution

Identify Like Terms

Like terms are terms that contain the same variables raised to the same power. In the given expression, $-18a$ and $-3a$ are like terms because they both contain the variable $a$ to the power of 1.

Combine Like Terms

Combine the like terms by adding or subtracting the coefficients. In this case, add the coefficients -18 and -3 to give -21.

Write Final Expression

The final simplified expression is -21 multiplied by $a$ which is $-21a$.

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Key Concepts

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

Understanding Like Terms

In algebra, recognizing like terms is essential for simplifying expressions. Like terms are terms that have the exact same variable parts. This means they have the same variable, like $ a $, and it's raised to the same power. In the expression $-18a - 3a$, both terms have the variable $ a $ raised to the first power. This makes them like terms because they share the same variable characteristics. Remember, only the coefficients, which are the numbers in front of the variables, can differ. Identifying like terms allows us to efficiently combine them to simplify expressions.

Combining Coefficients Effectively

Once like terms are identified, the next step is combining their coefficients. Coefficients are numbers that sit in front of the variables. In the expression $-18a - 3a$, the coefficients are $-18$ and $-3$. To combine these coefficients, you perform the operation indicated between them, which is addition or subtraction. Here, you add the coefficients: $-18 + (-3)$ to get $-21$. When combining coefficients, always keep the variable part the same. So, the terms $-18a$ and $-3a$ simplify to $-21a$ by adding their coefficients.

Simplifying Expressions Thoroughly

The goal of simplifying an algebraic expression is to make it as straightforward as possible by combining like terms. After identifying and combining the coefficients, you rewrite the expression using the new combined coefficient alongside the shared variable. For our example, once we鈥檝e combined $-18$ and $-3$ to get $-21$, the expression becomes $-21a$. This new expression is in its simplest form. Simplifying expressions helps in making complex calculations more manageable and is a foundational skill in algebra. It simplifies solving, graphing, and understanding equations.

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91影视

Simplify. $$-18 a-3 a$$

Short Answer

Step by step solution

Identify Like Terms

Combine Like Terms

Write Final Expression

Key Concepts

Understanding Like Terms

Combining Coefficients Effectively

Simplifying Expressions Thoroughly

One App. One Place for Learning.

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