/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 63 Simplify each expression. $$ ... [FREE SOLUTION] | 91影视

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Chapter 0: Problem 63

Simplify each expression. $$ -3(5)^{2}-(-2)(-8) $$

Short Answer

Expert verified
The simplified expression is \( -91 \).

Step by step solution

01

- Calculate the square

First, calculate \( (5)^{2} \ = 25 \).
02

- Multiply by -3

Now, multiply \( -3 \times 25 \) which gives \( -75 \).
03

- Calculate the product of negative numbers

Next, calculate \( -2 \times -8 \) which results in \( 16 \) because the product of two negative numbers is positive.
04

- Simplify the expression

Add the results from Step 2 and Step 3: \( -75 \ - 16 \) which simplifies to \( -75 - 16 = -91 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Exponents
Exponents play a critical role in algebra. They represent repeated multiplication of a number by itself. For instance, in the exercise given, we start with \( (5)^{2} \). This means we multiply 5 by itself: \( 5 \times 5 \), which results in 25.

Here are the key points to remember about exponents:
  • \( a^{2} = a \times a \): Squaring a number means multiplying it by itself.
  • \( a^{3} = a \times a \times a \): Cubing a number means multiplying it by itself three times.
  • \( a^{n} \): Indicates the number `a` is multiplied by itself `n` times.
Understanding the exponent process is essential for simplifying algebraic expressions.
Working with Negative Numbers
Negative numbers can sometimes be confusing, but mastering them is essential. When simplifying expressions, it's important to understand how negative numbers interact with other operations, especially multiplication and subtraction.

Here鈥檚 a brief guide:
  • Multiplying two negative numbers results in a positive number: \( -2 \times -8 = 16 \). Both negatives cancel each other out.
  • Multiplying a negative number with a positive number results in a negative number: \( -3 \times 25 = -75 \).
  • When subtracting a negative number, the negatives 'cancel' out, turning it into an addition: \( - (-8) \) is the same as adding \(+8\).
Always remember to keep a close eye on the signs when performing arithmetic operations involving negative numbers.
Basics of Multiplication
Multiplication is one of the most fundamental operations in algebra, and it's important to get comfortable with it. In the given problem, multiple instances of multiplication occur, such as \( -3 \times 25 \) and \( -2 \times -8 \).

Here are some critical multiplication concepts to keep in mind:
  • Multiplication is repeated addition: \( 3 \times 4 \) is the same as \( 4 + 4 + 4 \).
  • The order doesn鈥檛 matter: \( a \times b = b \times a \). This is called the commutative property.
  • Multiplying units: When dealing with algebraic expressions, multiplying constants (numerical values) and variables must follow the multiplication rules accurately.
Applying these basics correctly ensures that your algebraic simplifications, like the given problem, end up correctly.

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Most popular questions from this chapter

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Simplify each expression. $$ -8(\sqrt{64})-(-3)(-7) $$

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