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Chapter 1: Problem 93

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

Short Answer

Expert verified
The value of the expression is 72.

Step by step solution

01

Identify the given values

Given values are: \(x=6\), \(y=-4\), and \(a=3\).
02

Substitute the values into the expression

Replace \(x\), \(y\), and \(a\) with their given values in the expression \((2x + y)(3a)\). This gives us: \((2(6) + (-4))(3(3))\).
03

Simplify inside the parentheses

Simplify the expression inside the first parentheses: \(2(6) + (-4)\). This becomes: \(12 - 4 = 8\).
04

Multiply the simplified terms

Now we have \((8)(3(3))\). Calculate the inner multiplication first: \(3(3) = 9\), then multiply by 8: \(8 \times 9 = 72\).

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Key Concepts

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

Substitution
Substitution is a crucial first step in evaluating any algebraic expression. It involves replacing the variables in the expression with their given or known values. For instance, if the expression contains variables like \(x\), \(y\), and \(a\), and we know their values are 6, -4, and 3 respectively, we must substitute these numbers into the expression. This changes the algebraic terms into numerical terms, making them ready for further simplification and calculation. For example, the expression \((2x + y)(3a)\) becomes \((2(6) + (-4))(3(3))\) after substitution.
Simplification
Simplification is the process of combining like terms and performing arithmetic operations to condense the expression into a simpler form. After substitution, the expression \((2(6) + (-4))(3(3))\) is simplified step-by-step. First, handle the operations inside the parentheses. Calculate the first part: \(2(6) + (-4)\), which simplifies to \(12 - 4 = 8\). Simplifying each part of the expression individually helps in managing complex expressions easily. Simplification transforms the expression into a more straightforward numerical form, allowing for easier multiplication in the next steps.
Multiplication
Multiplication is the final step where we find the product of the simplified terms. After simplification, we have the expression \((8)(3(3))\). Here, we perform the inner multiplication first: \(3(3) = 9\). Using the order of operations (PEMDAS/BODMAS), it is crucial to handle inside-the-parentheses calculations first. Then multiply the result by the term outside: \(8 \times 9\). This results in a final product of 72. Multiplication combines the simplified values into one final numerical result, giving us the evaluated expression.

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Most popular questions from this chapter

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