Simplify The Expression: 8( 7x 8 ) =
Introduction
In mathematics, simplifying expressions is a crucial skill that helps us solve problems efficiently. When we encounter an expression like 8(7x + 8), our goal is to simplify it by applying the rules of arithmetic operations. In this article, we will delve into the world of algebra and explore the steps to simplify the given expression.
Understanding the Expression
The given expression is 8(7x + 8). To simplify it, we need to understand the order of operations, which is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is often remembered using the acronym PEMDAS, which stands for:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Applying the Order of Operations
Now that we understand the order of operations, let's apply it to the given expression. We have 8(7x + 8), which means we need to evaluate the expression inside the parentheses first.
Inside the parentheses, we have 7x + 8. To simplify this expression, we need to combine like terms. However, in this case, we don't have any like terms, so we can't simplify it further.
Distributing the 8
Now that we have evaluated the expression inside the parentheses, we can distribute the 8 to both terms inside the parentheses. This means we multiply 8 by 7x and 8 by 8.
Using the distributive property, we can write:
8(7x + 8) = 8(7x) + 8(8)
Simplifying the Expression
Now that we have distributed the 8, we can simplify the expression further. We have 8(7x) + 8(8), which can be simplified to:
56x + 64
Conclusion
In this article, we simplified the expression 8(7x + 8) by applying the order of operations and using the distributive property. We first evaluated the expression inside the parentheses, then distributed the 8 to both terms, and finally simplified the expression to 56x + 64. This example demonstrates the importance of following the order of operations and using algebraic properties to simplify expressions.
Frequently Asked Questions
- What is the order of operations? The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is often remembered using the acronym PEMDAS.
- How do I simplify an expression with parentheses? To simplify an expression with parentheses, we need to evaluate the expression inside the parentheses first, then apply the order of operations to the rest of the expression.
- What is the distributive property? The distributive property is a property of arithmetic that allows us to distribute a single value to multiple terms. For example, 8(7x + 8) = 8(7x) + 8(8).
Examples and Practice
Simplify the expression: 4(3x + 2)
- Simplify the expression: 2(5x - 3)
- Simplify the expression: 6(2x + 1)
Step-by-Step Solutions
- Simplify the expression: 4(3x + 2)
- Evaluate the expression inside the parentheses: 3x + 2
- Distribute the 4: 4(3x) + 4(2)
- Simplify the expression: 12x + 8
- Simplify the expression: 2(5x - 3)
- Evaluate the expression inside the parentheses: 5x - 3
- Distribute the 2: 2(5x) + 2(-3)
- Simplify the expression: 10x - 6
- Simplify the expression: 6(2x + 1)
- Evaluate the expression inside the parentheses: 2x + 1
- Distribute the 6: 6(2x) + 6(1)
- Simplify the expression: 12x + 6
Introduction
In our previous article, we simplified the expression 8(7x + 8) by applying the order of operations and using the distributive property. We first evaluated the expression inside the parentheses, then distributed the 8 to both terms, and finally simplified the expression to 56x + 64. In this article, we will answer some frequently asked questions related to simplifying expressions.
Q&A
Q: What is the order of operations?
A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is often remembered using the acronym PEMDAS, which stands for:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: How do I simplify an expression with parentheses?
A: To simplify an expression with parentheses, we need to evaluate the expression inside the parentheses first, then apply the order of operations to the rest of the expression.
Q: What is the distributive property?
A: The distributive property is a property of arithmetic that allows us to distribute a single value to multiple terms. For example, 8(7x + 8) = 8(7x) + 8(8).
Q: Can I simplify an expression with multiple parentheses?
A: Yes, you can simplify an expression with multiple parentheses by following the order of operations. First, evaluate the expressions inside the innermost parentheses, then work your way outwards.
Q: How do I handle negative numbers in expressions?
A: When working with negative numbers in expressions, remember that the negative sign can be distributed to both terms inside the parentheses. For example, -3(2x - 4) = -3(2x) + (-3)(-4).
Q: Can I simplify an expression with variables and constants?
A: Yes, you can simplify an expression with variables and constants by following the order of operations. First, evaluate any exponential expressions, then multiply and divide from left to right, and finally add and subtract from left to right.
Q: How do I simplify an expression with fractions?
A: When working with fractions in expressions, remember to multiply the numerator and denominator by the same value to eliminate the fraction. For example, 1/2(3x + 4) = (1/2)(3x) + (1/2)(4).
Examples and Practice
- Simplify the expression: 4(3x + 2)
- Simplify the expression: 2(5x - 3)
- Simplify the expression: 6(2x + 1)
Step-by-Step Solutions
- Simplify the expression: 4(3x + 2)
- Evaluate the expression inside the parentheses: 3x + 2
- Distribute the 4: 4(3x) + 4(2)
- Simplify the expression: 12x + 8 *ify the expression: 2(5x - 3)
- Evaluate the expression inside the parentheses: 5x - 3
- Distribute the 2: 2(5x) + 2(-3)
- Simplify the expression: 10x - 6
- Simplify the expression: 6(2x + 1)
- Evaluate the expression inside the parentheses: 2x + 1
- Distribute the 6: 6(2x) + 6(1)
- Simplify the expression: 12x + 6
Common Mistakes to Avoid
- Not following the order of operations
- Not distributing the value to both terms inside the parentheses
- Not simplifying the expression further after distributing the value
Conclusion
Simplifying expressions is an essential skill in mathematics, and it requires a clear understanding of the order of operations and the distributive property. By following the steps outlined in this article, you can simplify expressions with parentheses, variables, constants, and fractions. Remember to practice regularly to become proficient in simplifying expressions.