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Chapter 5: Problem 58

Evaluate each expression for the given replacement value. \(3 x^{2}\) if \(x\) is \(-1\)

Short Answer

Expert verified
The expression evaluates to 3.

Step by step solution

01

Substitution of Value

First, substitute the given value of \( x = -1 \) into the expression \( 3x^2 \). This will give us: \( 3(-1)^2 \).
02

Calculate the Square

Next, calculate the square of \( -1 \). Since \((-1)^2 = 1\), the expression will become \( 3 imes 1 \).
03

Final Multiplication

Multiply the 3 by the result of the squared value, 1. So, \( 3 imes 1 = 3 \).

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Key Concepts

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

Substitution in Algebra
Substitution in algebra involves replacing variables in an expression with actual numbers. This is an essential skill in evaluating algebraic expressions.
When faced with an expression such as \( 3x^2 \), and given a specific value for \( x \), the first step is to substitute that value into the expression.
For example, if \( x = -1 \), then substituting \( -1 \) for \( x \) transforms the expression to \( 3(-1)^2 \).
  • Identify the variable to be replaced, which is \( x \) in this case.
  • Replace the variable with its given value, \( -1 \).
  • Ensure that you use parentheses while substituting to avoid errors in calculation, especially with negative numbers.
By substituting accurately, you set the stage for correctly evaluating the whole expression.
Squaring Numbers
Squaring numbers is a fundamental arithmetic operation where a number is multiplied by itself. This operation is particularly important in algebra when dealing with expressions involving powers.
For the substituted expression \( 3(-1)^2 \), the part \((-1)^2\) needs to be evaluated next.
  • To square \(-1\), multiply \(-1\) by itself: \[ (-1) \times (-1) = 1 \].
  • Remember, a negative number squared always results in a positive number, because two negative signs cancel each other out during multiplication.
The outcome of the squaring step transforms the expression further to \( 3 \times 1 \), making it simpler for the final evaluations.
Evaluating Expressions
Evaluating expressions means finding their numerical value after all operations are performed. It involves following the correct order of operations: parentheses, exponents, multiplication and division (from left to right), and finally addition and subtraction (from left to right).
Once a number is substituted, and the power calculated, as in \( 3(-1)^2 \) transforming to \( 3 \times 1 \), the next step is straightforward multiplication.
  • Multiply the coefficient 3 by the result of the squared number: \[ 3 \times 1 = 3 \].
  • Conclude by writing the final value after confirming that all steps comply with the arithmetic operations rules.
Thus, evaluating an expression is about applying operations sequentially to arrive at a concrete value, which, in this instance, is 3.

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Most popular questions from this chapter

Divide If the divisor contains 2 or more terms, use long division. $$ \frac{x^{3}+6 x^{2}+18 x+27}{x+3} $$

Simplify each expression. See Section \(5.1 .\) $$ \frac{-48 a b^{6}}{32 a b^{3}} $$

Multiply each expression. $$ 2 a\left(a^{2}+1\right) $$

Multiply. See Example 7. $$ (b+3)\left(2 b^{2}+b-3\right) $$

Multiply each expression. $$ 4 y\left(y^{2}-8 y-4\right) $$
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