Problem 97 - Beginning and Intermediate Algebra

Question

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

Step-by-Step Solution

Answer

0

Step 1 - Substitute the variables

Substitute the given values into the expression: For the expression (6-x)(5+y)(3+a), substitute 6 for x, -4 for y, and 3 for a. So we have: (6-6)(5+(-4))(3+3)

Step 2 - Simplify inside the parentheses

Simplify the values inside each set of parentheses: (6-6) = 0, (5+(-4)) = 1, (3+3) = 6. Now the expression becomes: 0 * 1 * 6

Step 3 - Multiply the simplified values

Multiply the results from the simplified expression: 0 * 1 * 6 = 0.

Key Concepts

substitution in algebra

Substitution in algebra is the process of replacing variables in an expression with their given numerical values. This step is crucial as it allows us to transform an algebraic expression to a numerical one, making it easier to evaluate.

In our exercise, we were given specific values for the variables:

• \( x = 6 \)
• \( y = -4 \)
• \( a = 3 \)

To perform substitution, simply replace each variable in the expression i.e. \((6-x)(5+y)(3+a)\) with the provided values.

So, the expression becomes:
\((6-6)(5+(-4))(3+3)\).
This step is foundational for further simplification.

simplifying algebraic expressions

After substitution, the next crucial step is simplifying each part of the expression inside the parentheses. Simplification makes the expression less complex and prepares it for the final evaluation.

Here are the steps we took to simplify:

• We substituted 6 for x, -4 for y, and 3 for a: \((6-6)(5+(-4))(3+3)\)
• Then, we simplified each part inside the parentheses: \((6-6) = 0\), \((5+(-4)) = 1\), and \((3+3) = 6\)

Now, the expression became:
\(0 \times 1 \times 6\).
Simplifying inside the parentheses ensures that we are dealing with the simplest form of each component before proceeding to the final multiplication.

evaluating expressions step-by-step

Evaluating expressions step-by-step involves breaking down the problem into smaller, manageable parts. This methodical approach ensures accuracy and clarity.

For our given expression, here’s how we evaluated it step-by-step:

• First, we performed substitution: \((6-6)(5+(-4))(3+3)\)
• Next, we simplified inside the parentheses: \( (6-6) = 0 \), \( (5 + (-4)) = 1 \), \( (3+3) = 6 \)
• Finally, we multiplied the simplified values together: \(0 \times 1 \times 6 = 0\)

Performing each step carefully helps prevent mistakes and ensures that the final evaluated result is accurate. The final result for this exercise is 0.