Simplify The Expression:\[$(b+7)(2b+3)\$\]

by ADMIN 43 views

Simplify the Expression: (b+7)(2b+3)

In algebra, simplifying expressions is a crucial skill that helps us solve equations and inequalities. One of the most common methods of simplifying expressions is by using the distributive property, which states that for any real numbers a, b, and c, a(b + c) = ab + ac. In this article, we will use the distributive property to simplify the expression (b+7)(2b+3).

Understanding the Distributive Property

The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term in one expression by each term in another expression. For example, consider the expression (b+7)(2b+3). To simplify this expression, we need to multiply each term in the first expression (b+7) by each term in the second expression (2b+3).

Simplifying the Expression

To simplify the expression (b+7)(2b+3), we will use the distributive property to multiply each term in the first expression by each term in the second expression.

(b+7)(2b+3) = b(2b+3) + 7(2b+3)

Now, we will multiply each term in the first expression by each term in the second expression.

b(2b+3) = 2b^2 + 3b

7(2b+3) = 14b + 21

Now, we will combine the two expressions.

(b+7)(2b+3) = 2b^2 + 3b + 14b + 21

Combining Like Terms

Now that we have multiplied each term in the first expression by each term in the second expression, we can combine like terms to simplify the expression further.

2b^2 + 3b + 14b + 21 = 2b^2 + 17b + 21

In this article, we used the distributive property to simplify the expression (b+7)(2b+3). We multiplied each term in the first expression by each term in the second expression and then combined like terms to simplify the expression further. The final simplified expression is 2b^2 + 17b + 21.

Real-World Applications

Simplifying expressions is a crucial skill that has many real-world applications. In mathematics, simplifying expressions helps us solve equations and inequalities. In science, simplifying expressions helps us model real-world phenomena and make predictions. In engineering, simplifying expressions helps us design and optimize systems.

Tips and Tricks

Here are some tips and tricks to help you simplify expressions:

  • Use the distributive property: The distributive property is a powerful tool that helps us simplify expressions. Make sure to use it whenever possible.
  • Combine like terms: Combining like terms is an essential step in simplifying expressions. Make sure to combine like terms whenever possible.
  • Check your work: Always check your work to make sure that you have simplified the expression correctly.

Practice Problems

Here are some practice problems to help you practice simplifying expressions:

  • Simplify the expression: (x+5)(2x+3)
  • Simplify the expression: (y-3)(2y+4)
  • Simplify the expression: (z+2)(z-5)

In conclusion, simplifying expressions is a crucial skill that has many real-world applications. By using the distributive property and combining like terms, we can simplify expressions and solve equations and inequalities. Remember to always check your work and use the distributive property whenever possible. With practice and patience, you will become a master of simplifying expressions.
Simplify the Expression: (b+7)(2b+3) - Q&A

In our previous article, we used the distributive property to simplify the expression (b+7)(2b+3). In this article, we will answer some frequently asked questions about simplifying expressions.

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 in one expression by each term in another expression.

Q: How do I use the distributive property to simplify expressions?

A: To use the distributive property to simplify expressions, you need to multiply each term in one expression by each term in another expression. For example, consider the expression (b+7)(2b+3). To simplify this expression, you need to multiply each term in the first expression (b+7) by each term in the second expression (2b+3).

Q: What is the difference between the distributive property and the commutative property?

A: The distributive property and the commutative property are two different concepts in algebra. The distributive property allows us to expand expressions by multiplying each term in one expression by each term in another expression. The commutative property, on the other hand, allows us to rearrange the order of terms in an expression without changing the value of the expression.

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, consider the expression 2b^2 + 3b + 14b + 21. To combine like terms, you need to add the coefficients of the like terms: 2b^2 + (3b + 14b) + 21 = 2b^2 + 17b + 21.

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

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

  • Not using the distributive property: Failing to use the distributive property can lead to incorrect simplifications.
  • Not combining like terms: Failing to combine like terms can lead to incorrect simplifications.
  • Not checking work: Failing to check work can lead to incorrect simplifications.

Q: How do I check my work when simplifying expressions?

A: To check your work when simplifying expressions, you need to:

  • Re-read the problem: Re-read the problem to make sure you understand what is being asked.
  • Check your work: Check your work to make sure that you have simplified the expression correctly.
  • Use a calculator: Use a calculator to check your work and make sure that you have simplified the expression correctly.

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

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

  • Science: Simplifying expressions helps us model real-world phenomena and make predictions.
  • Engineering: Simplifying expressions helps us design and optimize systems.
  • Finance: Simplifying expressions helps us calculate interest rates and investment returns.

In conclusion, simplifying expressions is a crucial skill that has many real-world applications. By using the distributive property and combining like terms, we can simplify expressions and solve equations and inequalities. Remember to always check your work and use the distributive property whenever possible. With practice and patience, you will become a master of simplifying expressions.

Practice Problems

Here are some practice problems to help you practice simplifying expressions:

  • Simplify the expression: (x+5)(2x+3)
  • Simplify the expression: (y-3)(2y+4)
  • Simplify the expression: (z+2)(z-5)

Additional Resources

Here are some additional resources to help you practice simplifying expressions:

  • Algebra textbooks: Algebra textbooks provide a comprehensive overview of algebra and include many practice problems to help you practice simplifying expressions.
  • Online resources: Online resources, such as Khan Academy and Mathway, provide video lessons and practice problems to help you practice simplifying expressions.
  • Practice worksheets: Practice worksheets provide a set of practice problems to help you practice simplifying expressions.