What Is The Simplified Form Of The Expression? ( 3 X 2 + 5 X − 8 ) + ( 5 X 2 − 13 X − 5 (3x^2 + 5x - 8) + (5x^2 - 13x - 5 ( 3 X 2 + 5 X − 8 ) + ( 5 X 2 − 13 X − 5 ]A. 8 X 2 − 8 X − 13 8x^2 - 8x - 13 8 X 2 − 8 X − 13 B. 8 X 2 + 8 X − 13 8x^2 + 8x - 13 8 X 2 + 8 X − 13 C. 8 X 2 − X − 13 8x^2 - X - 13 8 X 2 − X − 13 D. 8 X 2 − 8 X + 13 8x^2 - 8x + 13 8 X 2 − 8 X + 13

Understanding the Problem

When dealing with algebraic expressions, combining like terms is a crucial step in simplifying the expression. In this problem, we are given two expressions: $(3x^2 + 5x - 8)$ and $(5x^2 - 13x - 5)$. Our goal is to find the simplified form of the expression obtained by adding these two expressions together.

Combining Like Terms

To simplify the expression, we need to combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have two types of like terms: terms with $x^2$, terms with $x$, and constant terms.

Step 1: Identify Like Terms

Let's identify the like terms in the given expressions:

• Terms with $x^2$: $3x^2$ and $5x^2$
• Terms with $x$: $5x$ and $-13x$
• Constant terms: $-8$ and $-5$

Step 2: Combine Like Terms

Now, let's combine the like terms:

• Terms with $x^2$: $(3x^2 + 5x^2) = 8x^2$
• Terms with $x$: $(5x - 13x) = -8x$
• Constant terms: $(-8 - 5) = -13$

Step 3: Simplify the Expression

By combining the like terms, we get the simplified expression: $8x^2 - 8x - 13$.

Conclusion

The simplified form of the expression $(3x^2 + 5x - 8) + (5x^2 - 13x - 5)$ is $8x^2 - 8x - 13$.

Answer

The correct answer is A. $8x^2 - 8x - 13$.

Why is this the Correct Answer?

This is the correct answer because we have correctly combined the like terms in the given expressions. The terms with $x^2$ are combined to get $8x^2$, the terms with $x$ are combined to get $-8x$, and the constant terms are combined to get $-13$. Therefore, the simplified form of the expression is $8x^2 - 8x - 13$.

What is the Importance of Simplifying Algebraic Expressions?

Simplifying algebraic expressions is an essential skill in mathematics. It helps us to:

• Reduce the complexity of the expression
• Make it easier to solve equations and inequalities
• Identify patterns and relationships between variables
• Make predictions and conclusions based on the expression

How to Simplify Algebraic Expressions?

To simplify algebraic expressions, we need to:

• Identify like terms
• Combine like terms
• Simplify the expression by removing any unnecessary terms or factors

Tips and Tricks

• Always start by identifying like terms
• Use the distributive property to expand expressions
• Combine like terms by adding or subtracting coefficients
• Simplify the expression by removing any unnecessary terms or factors

Common Mistakes to Avoid

• Failing to identify like terms
• Not combining like terms correctly
• Not simplifying the expression by removing unnecessary terms or factors

Conclusion

Simplifying algebraic expressions is a crucial skill in mathematics. By combining like terms and simplifying the expression, we can reduce the complexity of the expression and make it easier to solve equations and inequalities. Remember to always identify like terms, combine like terms, and simplify the expression by removing any unnecessary terms or factors.

Q: What is the first step in simplifying an algebraic expression?

A: The first step in simplifying an algebraic expression is to identify like terms. Like terms are terms that have the same variable raised to the same power.

Q: How do I identify like terms?

A: To identify like terms, look for terms that have the same variable and the same exponent. For example, in the expression $3x^2 + 5x^2$, the terms $3x^2$ and $5x^2$ are like terms because they both have the variable $x$ raised to the power of 2.

Q: What is the next step after identifying like terms?

A: After identifying like terms, the next step is to combine like terms. This involves adding or subtracting the coefficients of the like terms.

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients of the like terms. For example, in the expression $3x^2 + 5x^2$, the coefficients are 3 and 5. Adding these coefficients gives us $8x^2$.

Q: What is the final step in simplifying an algebraic expression?

A: The final step in simplifying an algebraic expression is to simplify the expression by removing any unnecessary terms or factors.

Q: What are unnecessary terms or factors?

A: Unnecessary terms or factors are terms or factors that do not affect the value of the expression. For example, in the expression $2x + 0$, the term $0$ is unnecessary because it does not affect the value of the expression.

Q: How do I simplify an expression by removing unnecessary terms or factors?

A: To simplify an expression by removing unnecessary terms or factors, look for terms or factors that are equal to zero or that can be canceled out. For example, in the expression $2x + 0$, we can simplify the expression by removing the term $0$.

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

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

• Failing to identify like terms
• Not combining like terms correctly
• Not simplifying the expression by removing unnecessary terms or factors

Q: How can I practice simplifying algebraic expressions?

A: You can practice simplifying algebraic expressions by working through examples and exercises in a textbook or online resource. You can also try simplifying expressions on your own and then checking your work with a calculator or online tool.

Q: What are some real-world applications of simplifying algebraic expressions?

A: Simplifying algebraic expressions has many real-world applications, including:

• Solving equations and inequalities in physics and engineering
• Modeling population growth and decay in biology
• Analyzing data and making predictions in statistics
• Creating and solving optimization problems in economics

Q: How can I use technology to simplify algebraic expressions?

A: You can use technology, such as calculators or computer algebra systems, to simplify algebraic expressions. These tools can help you identify like terms, combine like terms, and simplify expressions by removing unnecessary terms or factors.

Q: What are some tips for simplifying algebraic expressions?

A: Some tips for simplifying algebraic expressions include:

• Always start by identifying like terms
• Use the distributive property to expand expressions
• Combine like terms by adding or subtracting coefficients
• Simplify the expression by removing any unnecessary terms or factors

Q: How can I check my work when simplifying algebraic expressions?

A: You can check your work when simplifying algebraic expressions by using a calculator or computer algebra system to verify your answer. You can also try simplifying the expression in a different way to see if you get the same answer.