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Chapter 2: Problem 68

Evaluate the given expression for \(x=2, y=-3,\) and \(z=-4.\) $$z-3 x^{2}$$

Short Answer

Expert verified
-16

Step by step solution

01

- Substitute the values

Identify the values given: \(x = 2\), \(y = -3\), and \(z = -4\). Substitute these values into the expression \(z - 3x^{2}\).
02

- Simplify the Expression Inside the Exponent

Calculate the value of \(x^{2}\): \(2^{2} = 4\).
03

- Multiply by the Coefficient

Multiply the result by the coefficient: \(3 \times 4 = 12\).
04

- Combine the Results

Substitute the values back into the expression: \(z - 12\). With \(z = -4\), the expression becomes \(-4 - 12\).
05

- Final Calculation

Subtract 12 from -4 to get the final result: \(-4 - 12 = -16\).

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Key Concepts

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

Substitution
Substitution is one of the fundamental processes in algebra. It involves replacing the variables in an expression with their corresponding numerical values. For instance, given the expression \(z - 3x^2\) and the values \(x = 2\), \(y = -3\), and \(z = -4\), we substitute \(x\) and \(z\) into the expression.
Simplification
Simplification is about making an expression easier to work with. One of the key steps involves dealing with exponents and basic arithmetic. For our expression \(z - 3x^2\), once we substitute \(x = 2\), we need to simplify \(2^2\). This means calculating the exponent first, then performing the multiplication.
Exponents
Exponents denote repeated multiplication of a number by itself. In our expression, \(3x^2\) means \(3\) multiplied by \(x\) squared. For \(x = 2\), we need to compute \(2^2\), which equals 4. This exponentiation is then simplified further in the equation.
Basic Arithmetic Operations
Basic arithmetic operations include addition, subtraction, multiplication, and division. In simplifying our expression, we encounter multiplication first (\(3 \times 4 = 12\)). Then, we perform the subtraction: \(z - 12\) with \(z\) being \(-4\). This results in \(-4 - 12\), which equals \(-16\). Breaking it down into smaller, easier steps helps ensure accuracy in calculations.

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Most popular questions from this chapter

Simplify each expression as completely as possible. $$-a^{2}(3 a-7)-2 a\left[a^{2}-4(a-2)\right]$$

Examine each of the following expressions as given and determine the number of terms. Also find the coefficient and the literal part of each term. $$4 a(-5 b)$$

Evaluate the given expression for \(x=2, y=-3,\) and \(z=-4.\) $$y(x-z)^{2}$$

Simplify by combining like terms whenever possible. $$2 x^{2} y+x y^{2}-x^{2} y-x^{2} y-x y^{2}$$

Examine each of the following expressions as given and determine the number of terms. Also find the coefficient and the literal part of each term. $$4 x^{2}-3 x+2$$
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