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Chapter 1: Problem 84

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) $$ (5 x-2 y)(-2 a) $$

Short Answer

Expert verified
-228

Step by step solution

01

Substitute the given values

First, substitute the given values of the variables into the expression. The expression is \( (5x - 2y)(-2a) \). Replace \( x = 6, y = -4, \text{ and } a = 3 \). So the expression becomes \( (5(6) - 2(-4))(-2(3)) \).
02

Simplify inside the parentheses

Next, simplify the expressions inside each parentheses. For \( 5x - 2y \), calculate \( 5(6) - 2(-4) \). This results in \( 30 + 8 = 38 \). For \( -2a \), calculate \( -2(3) = -6 \).
03

Multiply the simplified expressions

Finally, multiply the simplified results together. Calculate \( 38(-6) \). This results in \( -228 \).

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Key Concepts

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

Substitution
Substitution is the process of replacing variables in an expression with given values. In algebra, this is an essential first step to solving problems involving equations or expressions. For instance, in our exercise, we started with the expression (5x - 2y)(-2a). The values given were: x = 6, y = -4, and a = 3. To substitute these values, we replace each variable with its corresponding number: (5(6) - 2(-4))(-2(3)). You simply insert the values in place of their respective variables. This makes the expression easier to work with, setting you up for the next steps.
Simplification
Simplification involves making an expression easier to read or work with by performing the arithmetic operations. After substituting the given values, you're left with the expression (5(6) - 2(-4))(-2(3)). Let's simplify the expression inside each parenthesis first:
  • Calculate 5(6), which equals 30.
  • Calculate -2(-4). Since a negative times a negative results in a positive, this equals 8.
Adding these together, we have: 30 + 8 = 38. Next, simplify the term -2a: Multiply -2 and 3, which results in -6. Now the expression looks like 38(-6), and we're set for the final step.
Multiplication of Expressions
Multiplication is the final step in our exercise. After simplifying the terms inside the parenthesis, we need to multiply them together. Our simplified expression is now 38(-6). Multiplying these terms together, perform the following calculation: 38 * (-6).
  • When multiplying a positive number by a negative number, the result is negative.
  • Simply multiply the absolute values: 38 * 6 = 228.
So the result is -228. Understanding each of these steps will help you tackle similar algebraic expressions with confidence. Substitution, simplification, and multiplication come together to make problem-solving more intuitive!

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