Simplify The Expression: { (x+10)(3x+10)$}$

$$

Introduction

In algebra, simplifying expressions is a crucial skill that helps in solving equations and inequalities. It involves combining like terms and removing any unnecessary components from the expression. In this article, we will simplify the given expression {(x+10)(3x+10)$}$ using the distributive property and combining like terms.

Understanding the Distributive Property

The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses. In the given expression, we have two binomials ${(x+10)}$ and ${(3x+10)}$ that need to be multiplied together.

Applying the Distributive Property

To simplify the expression, we will apply the distributive property by multiplying each term in the first binomial with each term in the second binomial.

${(x+10)(3x+10) = x(3x+10) + 10(3x+10)}$

Expanding the Terms

Now, we will expand each term by multiplying the terms inside the parentheses.

${x(3x+10) = 3x^2 + 10x}$

${10(3x+10) = 30x + 100}$

Combining Like Terms

Now that we have expanded each term, we can combine like terms to simplify the expression.

${3x^2 + 10x + 30x + 100}$

Simplifying the Expression

We can simplify the expression by combining the like terms ${10x}$ and ${30x}$ to get ${40x}$.

${3x^2 + 40x + 100}$

Final Answer

The simplified expression is ${3x^2 + 40x + 100}$.

Conclusion

In this article, we simplified the expression {(x+10)(3x+10)$}$ using the distributive property and combining like terms. We expanded each term by multiplying the terms inside the parentheses and then combined like terms to simplify the expression. This process is essential in algebra to solve equations and inequalities.

Tips and Tricks

• When simplifying expressions, always look for like terms to combine.
• Use the distributive property to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses.
• Be careful when combining like terms to avoid making mistakes.

Real-World Applications

Simplifying expressions is a crucial skill in many real-world applications, including:

• Physics: Simplifying expressions is essential in physics to solve equations and inequalities related to motion, energy, and momentum.
• Engineering: Simplifying expressions is crucial in engineering to design and optimize systems, such as electrical circuits and mechanical systems.
• Computer Science: Simplifying expressions is essential in computer science to optimize algorithms and data structures.

Common Mistakes

• Failing to combine like terms can lead to incorrect solutions.
• Not using the distributive property can result in incorrect expansions.
• Not checking the final answer can lead to errors.

Final Thoughts

Simplifying expressions is a fundamental skill in algebra that helps in solving equations and inequalities. By applying the distributive property and combining like terms, we can simplify expressions and arrive at the correct solution. Remember to always look for like terms to combine, use the distributive property to expand expressions, and be careful when combining like terms to avoid making mistakes.

$$

Introduction

In our previous article, we simplified the expression {(x+10)(3x+10)$}$ using the distributive property and combining like terms. In this article, we will answer some frequently asked questions related to simplifying expressions.

Q&A

Q: What is the distributive property?

A: The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses.

Q: How do I apply the distributive property?

A: To apply the distributive property, you need to multiply each term in the first binomial with each term in the second binomial.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, ${2x}$ and ${5x}$ are like terms because they both have the variable ${x}$ raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the like terms. For example, ${2x + 5x = 7x}$.

Q: What is the difference between the distributive property and combining like terms?

A: The distributive property is used to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses. Combining like terms is used to simplify expressions by adding or subtracting the coefficients of the like terms.

Q: Can I simplify expressions with more than two binomials?

A: Yes, you can simplify expressions with more than two binomials by applying the distributive property and combining like terms.

Q: How do I check my answer?

A: To check your answer, you need to plug in a value for the variable and see if the expression simplifies to the correct value.

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

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

• Failing to combine like terms
• Not using the distributive property
• Not checking the final answer

Tips and Tricks

• Always look for like terms to combine.
• Use the distributive property to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses.
• Be careful when combining like terms to avoid making mistakes.
• Check your answer by plugging in a value for the variable.

Real-World Applications

Simplifying expressions is a crucial skill in many real-world applications, including:

• Physics: Simplifying expressions is essential in physics to solve equations and inequalities related to motion, energy, and momentum.
• Engineering: Simplifying expressions is crucial in engineering to design and optimize systems, such as electrical circuits and mechanical systems.
• Computer Science: Simplifying expressions is essential in computer science to optimize algorithms and data structures.

Conclusion

Simplifying expressions is a fundamental skill in algebra that helps in solving equations and inequalities. By applying the distributive property and combining like terms, we can simplify expressions and arrive at the correct solution. Remember to always look for like terms to combine, use the distributive property to expand expressions, and be careful when combining like terms to avoid making mistakes.

Final Thoughts

Simplifying expressions is a crucial skill that helps in solving equations and inequalities. By understanding the distributive property and combining like terms, we can simplify expressions and arrive at the correct solution. Remember to always check your answer by plugging in a value for the variable and be careful when combining like terms to avoid making mistakes.