Problem 8 - Algebra 1

Question

Evaluate the expression when \(x=3\) $$ x^{2} $$

Step-by-Step Solution

Answer

The value of the expression \(x^{2}\) when \(x=3\) is 9.

Step 1: Identify the Expression and Value

The given expression is \(x^2\) and we want to find its value when \(x=3\).

Step 2: Substitute x with the given value

Replace the variable \(x\) in the expression with the given value. This gives us \((3)^2\).

Step 3: Simplify the expression

Computing \((3)^2\), we get \(3*3 = 9\).

Key Concepts

Understanding Substitution in Expressions

Substitution is a fundamental concept in mathematics that allows you to replace variables in expressions with specific values. Imagine you have a simple recipe and you are asked to use a particular ingredient amount instead of using general measurements. This is similar to substitution where we specify a value for the variable to perform the calculations.
In our exercise, the expression given is \(x^2\). We are asked to evaluate this expression when \(x = 3\). Through substitution, we replace \(x\) with 3, resulting in the expression \((3)^2\). When you see an expression asking for evaluation, substitution is your go-to process to insert values temporarily into the expressions. This helps to find a concrete number instead of leaving the expression abstract.

Working with Exponents

Exponents are a way of indicating that a number is to be multiplied by itself a certain number of times. It's like a quick shorthand for repeated multiplication. In the expression \(x^2\), the \(^2\) is an exponent, telling us that the base, \(x\), should be multiplied by itself once to get \(x \cdot x\).
Let's consider our exercise again: after substitution, we have \((3)^2\). The exponent \(^2\) here tells us to multiply 3 by itself, which looks like: \(3 \cdot 3\). Understanding exponents allows you to simplify and interpret expressions quickly and efficiently.
Exponents are also used to express very large or very small numbers conveniently. Keeping this in mind will make working with exponents straightforward as it opens various pathways in understanding many areas of math.

Step-by-Step Simplification: Arriving at the Answer

Simplification is crucial as it helps in condensing an expression down to its simplest form and makes it easier to understand or compute. After substituting and realizing the role of exponents, our next task is simplification.
In our example, we replace \(x\) with 3, which gives us \((3)^2 = 3 \cdot 3\). To simplify, we perform this multiplication to get 9. The process doesn't involve any complicated operations; simply carry out the arithmetic to achieve the final answer.
By breaking down the expression step-by-step, using substitution followed by evaluating the power indicated by exponents, you arrive at a simplified number. This method transforms expressions into understandable and manageable forms. It reinforces the practicality by yielding an answer to seemingly abstract mathematical problems.