Simplify The Expression.${ (-8)^2 - 4(1)(-5) }$Type Your Answer

Mar 8, 2025 by ADMIN 65 views

Simplify the Expression: A Step-by-Step Guide

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Introduction

In mathematics, simplifying expressions is a crucial skill that helps us solve problems efficiently. It involves combining like terms, removing parentheses, and performing operations in the correct order. In this article, we will simplify the expression $(-8)^2 - 4(1)(-5)$ using the order of operations and basic algebraic properties.

Understanding 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 acronym PEMDAS is commonly used to remember the order:

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.

Simplifying the Expression

Let's apply the order of operations to simplify the expression $(-8)^2 - 4(1)(-5)$ .

Step 1: Evaluate the Exponent

The first step is to evaluate the exponent $(-8)^2$ . According to the order of operations, we need to evaluate the expression inside the parentheses first.

$(-8)^2 = (-8) \times (-8) = 64$

Step 2: Multiply 4 and 1

Next, we need to multiply 4 and 1.

$4 \times 1 = 4$

Step 3: Multiply 4 and -5

Now, we need to multiply 4 and -5.

$4 \times (-5) = -20$

Step 4: Subtract -20 from 64

Finally, we need to subtract -20 from 64.

$64 - (-20) = 64 + 20 = 84$

Conclusion

In this article, we simplified the expression $(-8)^2 - 4(1)(-5)$ using the order of operations and basic algebraic properties. We evaluated the exponent, multiplied 4 and 1, multiplied 4 and -5, and finally subtracted -20 from 64. The simplified expression is 84.

Frequently Asked Questions

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 acronym PEMDAS is commonly used to remember the order.

Q: How do I simplify an expression?

A: To simplify an expression, you need to follow the order of operations. First, evaluate any expressions inside parentheses. Next, evaluate any exponential expressions. Then, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the difference between multiplication and division?

A: Multiplication and division are both operations that involve numbers. However, multiplication involves multiplying two or more numbers together, while division involves dividing one number by another.

Final Thoughts

Simplifying expressions is an essential skill in mathematics that helps us solve problems efficiently. By following the order of operations and basic algebraic properties, we can simplify even the most complex expressions. Remember to evaluate expressions inside parentheses first, then evaluate any exponential expressions, followed by multiplication and division operations, and finally addition and subtraction operations. With practice and patience, you will become proficient in simplifying expressions and solving mathematical problems with ease.

Additional Resources

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Introduction

In our previous article, we simplified the expression $(-8)^2 - 4(1)(-5)$ using the order of operations and basic algebraic properties. In this article, we will answer some frequently asked questions related to simplifying expressions.

Q&A

Q: What is the order of operations?

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?

Q: What is the difference between multiplication and division?

Q: Can I simplify an expression with multiple operations?

A: Yes, you can simplify an expression with multiple operations. Just follow the order of operations and perform the operations in the correct order.

Q: What if I have a negative number in an expression?

A: If you have a negative number in an expression, you need to follow the order of operations and perform the operations in the correct order. For example, if you have the expression $-3 \times 4$ , you need to multiply -3 and 4, which gives you -12.

Q: Can I simplify an expression with fractions?

A: Yes, you can simplify an expression with fractions. Just follow the order of operations and perform the operations in the correct order. For example, if you have the expression $\frac{1}{2} + \frac{1}{4}$ , you need to find a common denominator, which is 4. Then, you can add the fractions: $\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4}$ .

Q: What if I have a decimal number in an expression?

A: If you have a decimal number in an expression, you need to follow the order of operations and perform the operations in the correct order. For example, if you have the expression $3.5 \times 2$ , you need to multiply 3.5 and 2, which gives you 7.