Simplify The Expression:${ 2x(6x - 8) + 4x(1 + 8x) }$
Introduction
Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the steps involved in simplifying complex expressions. In this article, we will focus on simplifying the given expression: 2x(6x - 8) + 4x(1 + 8x). We will break down the expression into smaller parts, apply the distributive property, and combine like terms to simplify the expression.
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 sets of parentheses: (6x - 8) and (1 + 8x). We will apply the distributive property to each set of parentheses separately.
Distributive Property: 2x(6x - 8)
To simplify the expression 2x(6x - 8), we will multiply each term inside the parentheses with the term outside the parentheses. This can be written as:
2x(6x) - 2x(8)
Using the distributive property, we can rewrite this as:
12x^2 - 16x
Distributive Property: 4x(1 + 8x)
Similarly, to simplify the expression 4x(1 + 8x), we will multiply each term inside the parentheses with the term outside the parentheses. This can be written as:
4x(1) + 4x(8x)
Using the distributive property, we can rewrite this as:
4x + 32x^2
Combining Like Terms
Now that we have simplified each set of parentheses, we can combine like terms to simplify the expression further. We will add or subtract the coefficients of like terms to simplify the expression.
Combining Like Terms: 12x^2 - 16x + 4x + 32x^2
We can combine the like terms 12x^2 and 32x^2 by adding their coefficients:
12x^2 + 32x^2 = 44x^2
Similarly, we can combine the like terms -16x and 4x by adding their coefficients:
-16x + 4x = -12x
Final Simplified Expression
Now that we have combined like terms, we can write the final simplified expression:
44x^2 - 12x
This is the simplified expression of the given expression 2x(6x - 8) + 4x(1 + 8x).
Conclusion
Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the steps involved in simplifying complex expressions. In this article, we focused on simplifying the expression 2x(6x - 8) + 4x(1 + 8x) by applying the distributive property and combining like terms. We broke down the expression into smaller parts, applied the distributive property, and combined like terms to simplify the expression. The final simplified expression is 44x^2 - 12x.
Tips and Tricks
- When simplifying algebraic expressions, it's essential to apply the distributive property to each set of parentheses separately.
- When combining like terms, add or subtract the coefficients of like terms to simplify the expression.
- Always check your work by plugging in values or using a calculator to verify the simplified expression.
Common Mistakes to Avoid
- Failing to apply the distributive property to each set of parentheses separately.
- Failing to combine like terms correctly.
- Not checking the work by plugging in values or using a calculator to verify the simplified expression.
Real-World Applications
Simplifying algebraic expressions has numerous real-world applications in fields such as physics, engineering, and computer science. For example, in physics, simplifying algebraic expressions can help us solve problems related to motion, energy, and momentum. In engineering, simplifying algebraic expressions can help us design and optimize systems, such as electrical circuits and mechanical systems. In computer science, simplifying algebraic expressions can help us develop algorithms and data structures for solving complex problems.
Final Thoughts
Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the steps involved in simplifying complex expressions. By applying the distributive property and combining like terms, we can simplify expressions and solve problems in various fields. Remember to always check your work by plugging in values or using a calculator to verify the simplified expression. With practice and patience, you can become proficient in simplifying algebraic expressions and solving complex problems.
Introduction
In our previous article, we simplified the expression 2x(6x - 8) + 4x(1 + 8x) by applying the distributive property and combining like terms. In this article, we will answer some frequently asked questions (FAQs) related to simplifying algebraic 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, multiply each term inside the parentheses with the term outside the parentheses. For example, in the expression 2x(6x - 8), we multiply 2x with 6x and -8 separately.
Q: What are like terms?
A: Like terms are terms that have the same variable(s) raised to the same power. For example, 2x and 4x 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, add or subtract the coefficients of like terms. For example, in the expression 2x + 4x, we add the coefficients 2 and 4 to get 6x.
Q: What is the final simplified expression of 2x(6x - 8) + 4x(1 + 8x)?
A: The final simplified expression is 44x^2 - 12x.
Q: Can I use a calculator to simplify algebraic expressions?
A: Yes, you can use a calculator to simplify algebraic expressions. However, it's essential to understand the steps involved in simplifying complex expressions to ensure accuracy.
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 apply the distributive property, failing to combine like terms correctly, and not checking the work by plugging in values or using a calculator to verify the simplified expression.
Q: How can I practice simplifying algebraic expressions?
A: You can practice simplifying algebraic expressions by working on problems from textbooks, online resources, or worksheets. You can also try simplifying expressions on your own and then check your work using a calculator or by plugging in values.
Tips and Tricks
- Always apply the distributive property to each set of parentheses separately.
- Always combine like terms correctly.
- Always check your work by plugging in values or using a calculator to verify the simplified expression.
- Practice simplifying algebraic expressions regularly to become proficient.
Common Mistakes to Avoid
- Failing to apply the distributive property to each set of parentheses separately.
- Failing to combine like terms correctly.
- Not checking the work by plugging in values or using a calculator to verify the simplified expression.
Real-World Applications
Simplifying algebraic expressions has numerous real-world applications in fields such as physics, engineering, and computer science. For example, in physics, simplifying algebraic expressions can help us solve problems related to motion, energy, and momentum. In engineering, simplifying algebraic expressions can help us design and optimize systems, such as electrical circuits and mechanical systems. In computer science, simplifying algebraic expressions can help us develop algorithms and data structures for solving complex problems.
Final Thoughts
Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the steps involved in simplifying complex expressions. By applying the distributive property and combining like terms, we can simplify expressions and solve problems in various fields. Remember to always check your work by plugging in values or using a calculator to verify the simplified expression. With practice and patience, you can become proficient in simplifying algebraic expressions and solving complex problems.