Simplify The Expression. First, Use The Distributive Property.${ 8 + 4(2c - 1) }$ { 8 + 4(2c - 1) = \, \square \}

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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. This property is denoted by the formula:

a(b + c) = ab + ac

In this article, we will use the distributive property to simplify the given expression:

{ 8 + 4(2c - 1) \}

Step 1: Apply the Distributive Property

To simplify the expression, we will first apply the distributive property by multiplying each term inside the parentheses with the term outside. In this case, we have:

{ 8 + 4(2c - 1) \}

Using the distributive property, we can rewrite this expression as:

{ 8 + 4(2c) - 4(1) \}

Step 2: Simplify the Expression

Now that we have applied the distributive property, we can simplify the expression by combining like terms. In this case, we have:

{ 8 + 4(2c) - 4(1) \}

We can simplify this expression by multiplying 4 with 2c and -1:

{ 8 + 8c - 4 \}

Step 3: Combine Like Terms

Now that we have simplified the expression, we can combine like terms by adding or subtracting the coefficients of the same variables. In this case, we have:

{ 8 + 8c - 4 \}

We can combine the constant terms by adding 8 and -4:

{ 8c + 4 \}

The Final Answer

Therefore, the simplified expression is:

{ 8c + 4 \}

Conclusion

In this article, we used the distributive property to simplify the given expression. We applied the distributive property by multiplying each term inside the parentheses with the term outside, and then simplified the expression by combining like terms. The final answer is:

{ 8c + 4 \}

Example Use Case

The distributive property is a powerful tool in algebra that can be used to simplify complex expressions. For example, consider the expression:

{ 3(2x + 1) + 2(x - 1) \}

Using the distributive property, we can rewrite this expression as:

{ 6x + 3 + 2x - 2 \}

Simplifying this expression, we get:

{ 8x + 1 \}

Tips and Tricks

  • When applying the distributive property, make sure to multiply each term inside the parentheses with the term outside.
  • When simplifying an expression, look for like terms and combine them by adding or subtracting their coefficients.
  • Practice using the distributive property to simplify complex expressions.

Common Mistakes

  • Failing to apply the distributive property when simplifying an expression.
  • Not combining like terms when simplifying an expression.
  • Making errors when multiplying or adding terms.

Conclusion

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. This property is denoted by the formula:

a(b + c) = ab + ac

Q: How do I apply the distributive property?

A: To apply the distributive property, you need to multiply each term inside the parentheses with the term outside. For example, consider the expression:

{ 4(2x + 3) \}

Using the distributive property, we can rewrite this expression as:

{ 8x + 12 \}

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

A: The distributive property and the commutative property are two different properties in algebra. The distributive property allows us to expand expressions by multiplying each term inside the parentheses with the term outside, while the commutative property allows us to rearrange the order of terms in an expression without changing its value.

For example, consider the expression:

{ 3(2x + 1) \}

Using the distributive property, we can rewrite this expression as:

{ 6x + 3 \}

Using the commutative property, we can rearrange the order of terms in this expression as:

{ 3 + 6x \}

Q: How do I simplify an expression using the distributive property?

A: To simplify an expression using the distributive property, you need to follow these steps:

  1. Apply the distributive property by multiplying each term inside the parentheses with the term outside.
  2. Simplify the expression by combining like terms.
  3. Check your work by plugging in values for the variables.

For example, consider the expression:

{ 8 + 4(2x - 1) \}

Using the distributive property, we can rewrite this expression as:

{ 8 + 8x - 4 \}

Simplifying this expression, we get:

{ 8x + 4 \}

Q: What are some common mistakes to avoid when using the distributive property?

A: Some common mistakes to avoid when using the distributive property include:

  • Failing to apply the distributive property when simplifying an expression.
  • Not combining like terms when simplifying an expression.
  • Making errors when multiplying or adding terms.

Q: How do I practice using the distributive property?

A: To practice using the distributive property, you can try the following exercises:

  • Simplify expressions using the distributive property.
  • Apply the distributive property to complex expressions.
  • Check your work by plugging in values for the variables.

Q: What are some real-world applications of the distributive property?

A: The distributive property has many real-world applications, including:

  • Simplifying complex expressions in algebra.
  • Solving systems of equations.
  • Modeling real-world problems using mathematical equations.

Conclusion

In conclusion, the distributive property is a fundamental concept in algebra that allows us to simplify complex expressions. By applying the distributive property and combining like terms, we can simplify expressions and arrive at the final answer. Remember to practice using the distributive property to simplify complex expressions, and avoid common mistakes such as failing to apply the distributive property or not combining like terms.