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Substitution is a fundamental concept in algebra where you replace variables with given numeric values to simplify or solve expressions and equations. In the exercise, the expression given is \(2x^3\), and the task is to evaluate it for \(x = -1\). The process starts by directly substituting \(x\) with the given value. Therefore, the expression \(2x^3\) becomes \(2(-1)^3\).Substitution is often the first step in solving many algebraic problems. It allows you to transform an algebraic expression into a numerical one, which can then be calculated using basic arithmetic operations. Steps you'll often go through include:

• Identification of the variable to substitute.
• Replacement of the variable with a given value.
• Re-evaluating the expression with the substituted value.

Approaching problems with this method can make complicated expressions more manageable and lead to a clearer path to the solution.

When you cube a number, you are raising it to the power of three. This means multiplying the number by itself twice more. Cubing negative numbers can be tricky for some students. It's important to remember:

• For any negative number, the cube will also be negative because a negative times a negative (which is positive) times a negative (again negative) results in a negative answer.

In the exercise, you need to calculate \((-1)^3\). Here's how it goes:

• First, multiply \(-1\) by \(-1\), which equals 1.
• Then, multiply the result by \(-1\) again to get \(-1\).

Cubing preserves the sign of the original number because of the odd power. Understanding this property helps address similar questions across different problems.

Understanding and applying the order of operations correctly is crucial in algebra. Often noted by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), it dictates the sequence in which mathematical operations are performed to ensure consistent results.Starting with substitution, as seen in our example, the next step focuses on the exponent first, as indicated by PEMDAS. In the expression \(2(-1)^3\):

• The cubing, or exponent operation, occurs first: \((-1)^3 = -1\).

Once the exponent has been dealt with, the next operation, according to the order of operations, is multiplication:

• Multiply \(2\) by the result of the cubing, \(-1\), to obtain \(-2\).

Following these rules ensures that even complex expressions are solved in a logically consistent manner, leading to correct answers across algebraic calculations.