Problem 35 Combine like terms. $$ 4 m w... [FREE SOLUTION]

Chapter 1: Problem 35

Combine like terms. $$ 4 m w^{2}-15 m w^{2} $$

Short Answer

Expert verified

-11mw^{2}

Step by step solution

Identify Like Terms

Like terms are terms that have the same variables raised to the same powers. In this case, both terms have the variables and exponents: $ mw^{2} $.

Combine Coefficients

To combine the like terms, add or subtract their coefficients. Here, the coefficients are 4 and -15. Compute: $4 - 15 = -11$.

Write the Result

Combine the result from Step 2 with the variable part $ mw^{2} $: $-11mw^{2} $.

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Key Concepts

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

Coefficients

Coefficients are the numbers in front of the variables in an algebraic term. They tell us how many of that term we have. For example, in the term $4mw^{2}$, 4 is the coefficient. It's like saying we have 4 of the $mw^{2}$ term.
To combine like terms, we focus on the coefficients. We add or subtract them based on the problem's requirements. In our example exercise, the coefficients are 4 and -15. When we combine these, we get -11. So, $4 - 15 = -11$.
Understanding coefficients is crucial because it allows us to simplify expressions and solve equations more easily. Always remember, coefficients give us the quantity of the variable part they are attached to.

Like Terms

Like terms are terms that contain the same variables raised to the same power. For instance, $4mw^{2}$ and $-15mw^{2}$ are like terms because they both have $mw^{2}$ as their variable expression.
To simplify an expression, we combine like terms by adding or subtracting their coefficients. This step significantly reduces the complexity of variable expressions, making them easier to work with.
Remember, you can only combine terms that are exactly alike. Terms like $3x$ and $5y$ or $x^2$ and $x$ are not like terms, so they cannot be combined.

Variable Expressions

Variable expressions are mathematical phrases that include numbers, variables, and operation symbols. For example, $4mw^{2}$ is a variable expression where we have a coefficient (4), variables (m and w), and an exponent (2).
In algebra, simplifying variable expressions by combining like terms can simplify our calculations. This makes it easier to solve equations or understand mathematical relationships.
When working with variable expressions, always ensure that you properly identify and combine like terms according to the rules of algebra. This prevents mistakes and leads to correct and simplified results, such as transforming $4mw^{2} - 15 mw^{2}$ into $-11mw^{2}$.

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91影视

Combine like terms. $$ 4 m w^{2}-15 m w^{2} $$

Short Answer

Step by step solution

Identify Like Terms

Combine Coefficients

Write the Result

Key Concepts

Coefficients

Like Terms

Variable Expressions

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