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Chapter 1: Problem 88

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

Short Answer

Expert verified
The value of the expression is 0.

Step by step solution

01

- Substitute the values

First, replace the variables in the expression with their given values. We have: \[ x=6, y=-4, a=3 \]Substitute these values into the expression: \[ (6-x)(5+y)(3+a) \]This becomes: \[ (6-6)(5+(-4))(3+3) \]
02

- Simplify each term

Now, simplify each term inside the parentheses: \[ (6-6) = 0 \]\[ (5 + (-4)) = 1 \]\[ (3 + 3) = 6 \]
03

- Multiply the simplified terms

Next, multiply these simplified values together: \[ 0 \times 1 \times 6 = 0 \]

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Key Concepts

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

Substitution Method
The substitution method involves replacing the variables in an algebraic expression with specific values. In the given problem, values for variables were provided: \( x=6, y=-4, a=3 \). By substituting these values into the expression \( (6-x)(5+y)(3+a) \), we transform it to: \( (6-6)(5+(-4))(3+3) \). This step is crucial as it allows us to directly work with numbers instead of variables.
Simplifying Expressions
Simplifying expressions involves reducing each term to its simplest form. After substitution in the example, we need to simplify each part of the expression:
  • \( (6-6) = 0 \)
  • \( (5+(-4)) = 1 \)
  • \( (3+3) = 6 \)
Breaking down each component step-by-step ensures accuracy and makes the expression easier to manage. By simplifying, we've converted the complex expression into manageable numerical terms ready for multiplication.
Multiplication of Integers
Once the expression is simplified, the next step is multiplying the integers. Our simplified terms from the exercise are: 0, 1, and 6. The final step is to multiply these numbers: \( 0 \times 1 \times 6 \). It's important to remember some basic properties of multiplication:
  • Any number multiplied by 0 is 0 (zero property of multiplication).
  • The order of multiplication does not matter (commutative property).
Therefore, \( 0 \times 1 \times 6 = 0 \). This makes it clear that multiplying any number by zero results in zero as the final answer.

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Most popular questions from this chapter

To find the average (mean) of numbers, we add the numbers and then divide the sum by the number of terms added. For example, to find the average of \(14,8,3,9,\) and \(1,\) we add them and then divide by 5. $$ \frac{14+8+3+9+1}{5}=\frac{35}{5}=7 \leftarrow \text { Average } $$ Find the average of each group of numbers. \(18,12,0,-4,\) and \(-10\)

Perform each indicated operation. $$ \frac{-13(-4)-(-8)(-2)}{(-10)(2)-4(-2)} $$

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

Write a numerical expression for each phrase and simplify. Twice the product of \(-1\) and \(6,\) subtracted from \(-4\)

Write a numerical expression for each phrase and simplify. Three subtracted from the product of 4.2 and \(-8.5\)
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