Problem 103 Simplify. $$ 3 a^{2} w^{2}-5... [FREE SOLUTION]

Chapter 1: Problem 103

Simplify. $$ 3 a^{2} w^{2}-5 w^{2} \cdot a^{2}-2 a w \cdot 2 a w $$

Short Answer

Expert verified

-6a^{2}w^{2}

Step by step solution

- Identify like terms

Look at each term: 1. The first term is $3a^{2}w^{2}$.2. The second term is $-5w^{2}a^{2}$, which is the same as $-5a^{2}w^{2}$.3. The third term is $-2aw \cdot 2aw$, which simplifies to $-4a^{2}w^{2}$.

- Combine like terms

Add the coefficients of like terms:Combine $3a^{2}w^{2} - 5a^{2}w^{2} - 4a^{2}w^{2}$.This is equivalent to $(3 - 5 - 4)a^{2}w^{2}$.

- Simplify the expression

Calculate the combined coefficient:$3 - 5 - 4 = -6$.Therefore, the simplified expression is $-6a^{2}w^{2}$.

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Key Concepts

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

Combining Like Terms

When simplifying algebraic expressions, combining like terms is a crucial step. Like terms have the same variables raised to the same powers. For example, in our exercise, the terms $3a^{2}w^{2}$ and $-5a^{2}w^{2}$ are like terms because they both have the variables $a$ and $w$ raised to the power of 2. To combine like terms, you simply add or subtract their coefficients. This way, you reduce the complexity of the polynomial and make it easier to work with. In our given problem, we first identified the like terms, $3a^{2}w^{2}$, $-5a^{2}w^{2}$, and $-4a^{2}w^{2}$, and then combined them to simplify the expression.

Coefficients

Coefficients are the numerical factors in terms of an algebraic expression. They are the numbers in front of the variables. For instance, in the term $3a^{2}w^{2}$, the coefficient is 3. Combining like terms often involves working with their coefficients. In our example, we had coefficients 3, -5, and -4 from the terms $3a^{2}w^{2}$, $-5a^{2}w^{2}$, and $-4a^{2}w^{2}$, respectively. By adding these coefficients together (\text{3} - \text{5} - \text{4}), we get a single coefficient of -6. This allows us to write the simplified term as $-6a^{2}w^{2}$.

Polynomial Simplification

Polynomial simplification involves reducing an expression to its simplest form. This includes combining like terms and ensuring that all coefficients are as simplified as possible. Let's break down the solution step by step:

First, we identified all like terms: $3a^{2}w^{2}$, $-5a^{2}w^{2}$, and $-4a^{2}w^{2}$.

Next, we combined these like terms by adding their coefficients: $3 - 5 - 4 = -6$.

Finally, we rewrote the expression using the new coefficient, resulting in $-6a^{2}w^{2}$.

Now, we have the simplified polynomial, which is much easier to understand and work with. Polynomial simplification is an essential skill for solving more complex algebraic problems confidently.

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91影视

Simplify. $$ 3 a^{2} w^{2}-5 w^{2} \cdot a^{2}-2 a w \cdot 2 a w $$

Short Answer

Step by step solution

- Identify like terms

- Combine like terms

- Simplify the expression

Key Concepts

Combining Like Terms

Coefficients

Polynomial Simplification

One App. One Place for Learning.

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