Simplify The Expression: ( 5 X 3 − 3 X 2 + 4 X ) + ( 3 X 3 − 7 X 2 + X ) = \left(5x^3 - 3x^2 + 4x\right) + \left(3x^3 - 7x^2 + X\right) = ( 5 X 3 − 3 X 2 + 4 X ) + ( 3 X 3 − 7 X 2 + X ) =

Introduction

In algebra, combining like terms is a fundamental concept that helps simplify complex expressions. It involves adding or subtracting terms that have the same variable and exponent. In this article, we will simplify the given expression by combining like terms.

The Expression

The given expression is:

$\left(5x^3 - 3x^2 + 4x\right) + \left(3x^3 - 7x^2 + x\right)$

Step 1: Identify Like Terms

To simplify the expression, we need to identify like terms. Like terms are terms that have the same variable and exponent. In this expression, we can identify the following like terms:

• $5x^3$ and $3x^3$
• $-3x^2$ and $-7x^2$
• $4x$ and $x$

Step 2: Combine Like Terms

Now that we have identified the like terms, we can combine them. To combine like terms, we add or subtract the coefficients of the terms.

• For the $x^3$ terms, we add the coefficients: $5x^3 + 3x^3 = 8x^3$
• For the $x^2$ terms, we add the coefficients: $-3x^2 - 7x^2 = -10x^2$
• For the $x$ terms, we add the coefficients: $4x + x = 5x$

Step 3: Simplify the Expression

Now that we have combined the like terms, we can simplify the expression by adding the resulting terms.

$\left(5x^3 - 3x^2 + 4x\right) + \left(3x^3 - 7x^2 + x\right) = 8x^3 - 10x^2 + 5x$

Conclusion

In this article, we simplified the given expression by combining like terms. We identified the like terms, combined them, and simplified the expression. This process helps to simplify complex expressions and make them easier to work with.

Tips and Tricks

• When combining like terms, make sure to add or subtract the coefficients of the terms.
• Use the distributive property to expand expressions and make it easier to identify like terms.
• Simplify expressions by combining like terms to make them easier to work with.

Real-World Applications

Combining like terms is a fundamental concept in algebra that has many real-world applications. It is used in various fields such as physics, engineering, and economics to simplify complex expressions and make them easier to work with.

Example Problems

• Simplify the expression: $\left(2x^2 + 3x - 4\right) + \left(x^2 - 2x + 5\right)$
• Simplify the expression: $\left(4x^3 - 2x^2 + 3x\right) + \left(2x^3 + 4x^2 - 2x\right)$

Answer Key

• $\left(2x^2 + 3x - 4\right) + \left(x^2 - 2x + 5\right) = 3x^2 + x + 1$
• $\left(4x^3 - 2x^2 + 3x\right) + \left(2x^3 + 4x^2 - 2x\right) = 6x^3 + 2x^2 + x$

Conclusion

Introduction

Combining like terms is a fundamental concept in algebra that helps simplify complex expressions. In our previous article, we provided a step-by-step guide on how to combine like terms. In this article, we will answer some frequently asked questions about combining like terms.

Q: What are like terms?

A: Like terms are terms that have the same variable and exponent. For example, $2x^2$ and $3x^2$ are like terms because they have the same variable ($x$) and exponent ($2$).

Q: How do I identify like terms?

A: To identify like terms, you need to look for terms that have the same variable and exponent. You can also use the distributive property to expand expressions and make it easier to identify like terms.

Q: What is the distributive property?

A: The distributive property is a mathematical property that allows you to expand expressions by multiplying each term inside the parentheses by the factor outside the parentheses. For example, $2(x + 3) = 2x + 6$.

Q: How do I combine like terms?

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

Q: What if I have a negative coefficient?

A: If you have a negative coefficient, you need to subtract the coefficient from the other term. For example, if you have $-2x^2$ and $3x^2$, you can combine them by subtracting the coefficients: $-2x^2 + 3x^2 = x^2$.

Q: Can I combine terms with different variables?

A: No, you cannot combine terms with different variables. For example, $2x^2$ and $3y^2$ are not like terms because they have different variables ($x$ and $y$).

Q: Can I combine terms with different exponents?

A: No, you cannot combine terms with different exponents. For example, $2x^2$ and $3x^3$ are not like terms because they have different exponents ($2$ and $3$).

Q: What if I have a term with a variable and a constant?

A: If you have a term with a variable and a constant, you can combine it with other terms that have the same variable. For example, if you have $2x$ and $3x$, you can combine them by adding the coefficients: $2x + 3x = 5x$.

Q: Can I combine terms with fractions?

A: Yes, you can combine terms with fractions. For example, if you have $\frac{1}{2}x^2$ and $\frac{3}{2}x^2$, you can combine them by adding the coefficients: $\frac{1}{2}x^2 + \frac{3}{2}x^2 = 2x^2$.

Conclusion

In conclusion, combining like terms is a fundamental concept in algebra that helps simplify complex expressions. By identifying like terms, combining them, and simplifying the expression, you can make complex expressions easier to work with. We hope this Q&A guide has helped you understand combining like terms better.

Tips and Tricks

• Make sure to identify like terms before combining them.
• Use the distributive property to expand expressions and make it easier to identify like terms.
• Simplify expressions by combining like terms to make them easier to work with.

Real-World Applications

Combining like terms is a fundamental concept in algebra that has many real-world applications. It is used in various fields such as physics, engineering, and economics to simplify complex expressions and make them easier to work with.

Example Problems

• Simplify the expression: $\left(2x^2 + 3x - 4\right) + \left(x^2 - 2x + 5\right)$
• Simplify the expression: $\left(4x^3 - 2x^2 + 3x\right) + \left(2x^3 + 4x^2 - 2x\right)$

Answer Key

• $\left(2x^2 + 3x - 4\right) + \left(x^2 - 2x + 5\right) = 3x^2 + x + 1$
• $\left(4x^3 - 2x^2 + 3x\right) + \left(2x^3 + 4x^2 - 2x\right) = 6x^3 + 2x^2 + x$