Find The Sum Or Difference. Write Your Answer In Standard Form. \left(2h^2 - \frac{5}{3}h\right) + \left(\frac{11}{3}h - 3h^2\right ]

Mar 12, 2025 by ADMIN 134 views

Find the Sum or Difference: Simplifying Algebraic Expressions

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Introduction

In algebra, simplifying expressions is a crucial step in solving equations and manipulating mathematical statements. When dealing with expressions that involve addition or subtraction, it's essential to combine like terms to simplify the expression. In this article, we will explore how to find the sum or difference of two algebraic expressions and write the result in standard form.

Understanding the Problem

The given problem involves finding the sum of two algebraic expressions:

$\left(2h^2 - \frac{5}{3}h\right) + \left(\frac{11}{3}h - 3h^2\right)$

To simplify this expression, we need to combine like terms, which involves adding or subtracting the coefficients of the same variables.

Combining Like Terms

Like terms are terms that have the same variable raised to the same power. In the given expression, we can identify the following like terms:

$2h^2$ and $-3h^2$
$-\frac{5}{3}h$ and $\frac{11}{3}h$

To combine these like terms, we need to add or subtract their coefficients.

Simplifying the Expression

Let's simplify the expression by combining the like terms:

$\left(2h^2 - \frac{5}{3}h\right) + \left(\frac{11}{3}h - 3h^2\right)$

$= 2h^2 - 3h^2 - \frac{5}{3}h + \frac{11}{3}h$

$= -h^2 + \frac{6}{3}h$

$= -h^2 + 2h$

The simplified expression is $-h^2 + 2h$ .

Writing the Result in Standard Form

The standard form of an algebraic expression is the form in which the variables are written in descending order of their powers. In the simplified expression $-h^2 + 2h$ , the variable $h$ is written in descending order of its power.

Conclusion

In this article, we learned how to find the sum or difference of two algebraic expressions and write the result in standard form. We identified like terms, combined them, and simplified the expression. The final result is $-h^2 + 2h$ , which is written in standard form.

Tips and Tricks

When combining like terms, make sure to add or subtract the coefficients of the same variables.
Use the distributive property to simplify expressions that involve multiplication or division.
Check your work by plugging in values for the variables and simplifying the expression.

Example Problems

Find the sum of the following expressions: $\left(4x^2 + 3x\right) + \left(2x^2 - 5x\right)$
Find the difference of the following expressions: $\left(3y^2 + 2y\right) - \left(2y^2 - 4y\right)$

Practice Problems

Find the sum of the following expressions: $\left(2a^2 - 3a\right) + \left(a^2 + 4a\right)$
Find the difference of the following expressions: $\left(5b^2 + 2b\right) - \left(3b^2 - 6b\right)$

Final Thoughts

Simplifying algebraic expressions is an essential skill in mathematics. By combining like terms and writing the result in standard form, we can simplify complex expressions and solve equations. Practice makes perfect, so be sure to try the example problems and practice problems to reinforce your understanding of this concept.

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Introduction

In our previous article, we explored how to find the sum or difference of two algebraic expressions and write the result in standard form. In this article, we will answer some frequently asked questions related to this topic.

Q&A

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, $2x^2$ and $-3x^2$ are like terms because they both have the variable $x$ raised to the power of 2.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract their coefficients. For example, if you have the expression $2x^2 + 3x^2$ , you can combine the like terms by adding their coefficients: $2x^2 + 3x^2 = 5x^2$ .

Q: What is the standard form of an algebraic expression?

A: The standard form of an algebraic expression is the form in which the variables are written in descending order of their powers. For example, the expression $-h^2 + 2h$ is in standard form because the variable $h$ is written in descending order of its power.

Q: How do I simplify an expression that involves addition or subtraction?

A: To simplify an expression that involves addition or subtraction, you need to combine like terms and then simplify the resulting expression. For example, if you have the expression $\left(2h^2 - \frac{5}{3}h\right) + \left(\frac{11}{3}h - 3h^2\right)$ , you can simplify it by combining the like terms and then simplifying the resulting expression.

Q: What are some common mistakes to avoid when simplifying expressions?

A: Some common mistakes to avoid when simplifying expressions include:

Not combining like terms
Adding or subtracting coefficients incorrectly
Not simplifying the resulting expression
Not checking the work by plugging in values for the variables

Q: How can I practice simplifying expressions?

A: You can practice simplifying expressions by working through example problems and practice problems. You can also try simplifying expressions on your own and then check your work by plugging in values for the variables.

Tips and Tricks

Make sure to combine like terms carefully to avoid making mistakes.
Use the distributive property to simplify expressions that involve multiplication or division.
Check your work by plugging in values for the variables and simplifying the expression.