Problem 39 Combine like terms. Write each a... [FREE SOLUTION]

Chapter 15: Problem 39

Combine like terms. Write each answer in descending order. $$ 3 x^{3}-x^{2}+x^{4}+x^{2} $$

Short Answer

Expert verified

The simplified expression is $x^4 + 3x^3$.

Step by step solution

Identify Like Terms

List out the terms: $3x^3$, $-x^2$, $x^4$, and $x^2$. Terms that have the same variable raised to the same power are like terms.

Combine Like Terms

Combine the like terms: $-x^2$ and $x^2$. These cancel out each other: $-x^2 + x^2 = 0$. So we are left with $3x^3$ and $x^4$.

Arrange in Descending Order

Write the remaining terms in descending order of their exponents. The term with the highest exponent is $x^4$ followed by $3x^3$. Thus, the expression simplifies to $x^4 + 3x^3$.

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Key Concepts

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

Descending Order

When arranging terms in an algebraic expression, it's typical to write them in descending order. This means organizing from the highest power to the lowest.
For instance, in the expression given:

First, you have to identify the exponents of each term.
Next, arrange these terms so that the term with the highest exponent comes first, followed by the terms with progressively lower exponents.
The given expression is: \[3x^3 - x^2 + x^4 + x^2\]

In this case, the term $x^4$ has the highest exponent (4), followed by $3x^3$, $-x^2$, and finally the other $x^2$. Once combined and simplified, the arrangement should look like this: \[x^4 + 3x^3\]
Remember, organizing terms in descending order makes the expression easier to read and understand.

Like Terms

Like terms are terms that have the same variable raised to the same power.
For example, in the expression: \[3x^3 - x^2 + x^4 + x^2\]
The like terms are:

$-x^2$ and $x^2$ because they both have the variable $x$ raised to the power of 2.

To combine like terms:

Add or subtract the coefficients of the like terms. Here, we combine $-x^2$ and $x^2$ which results in: \[-x^2 + x^2 = 0\]

This step is crucial to simplifying expressions and making them more manageable.

Algebraic Simplification

Algebraic simplification involves reducing an expression into its simplest form. Here鈥檚 how you do it:

First, identify all the like terms and combine them in the expression:

Expression: \[3x^3 - x^2 + x^4 + x^2\]
Combine like terms: \[-x^2 + x^2\] to get: \[0\]
Now you are left with: \[3x^3\textrm{ and }x^4\]

For the final step, arrange these simplified terms in descending order to get: \[x^4 + 3x^3\]

This simplification makes it easier to work with algebraic expressions in further calculations or applications.

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91影视

Combine like terms. Write each answer in descending order. $$ 3 x^{3}-x^{2}+x^{4}+x^{2} $$

Short Answer

Step by step solution

Identify Like Terms

Combine Like Terms

Arrange in Descending Order

Key Concepts

Descending Order

Like Terms

Algebraic Simplification

One App. One Place for Learning.

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