Problem 62 - Algebra 1

Question

Evaluate the expression when \(x=2\). $$ (x)(x) $$

Step-by-Step Solution

Answer

The evaluated expression is 4.

Step 1: Substitute the given value of the variable into the expression

The expression provided is \((x)(x)\). Replace each occurrence of \(x\) in the expression with the given value which is 2, leading to \((2)(2)\).

Step 2: Perform the multiplication

Now, calculate the multiplication of the two 2's which results in 4.

Key Concepts

Substitution

Substitution is a technique used in algebra that helps simplify and solve equations and expressions. When substituting, you replace a variable with a given number. In our exercise, the variable is represented by the letter "x." This means wherever you see "x," you'll replace it with the specific value provided.

For this problem, the value given is 2. So, the expression originally written as \((x)(x)\) becomes \((2)(2)\) after substitution. It's like changing a player in a game; the entity remains the same, but its representation is switched.

By substituting, you're taking away the abstraction of the variable and applying a real number, which makes it easier to carry out further calculations. This fundamental skill is crucial in solving algebraic expressions and equations efficiently.

Multiplication

Once substitution is complete, it's time to work out the math with multiplication, which is the next step in the process. When we multiply two numbers – in this case, 2 and 2 – we find the product of these numbers.

Multiplication is essentially repeated addition. Here, multiplying two twos can be visualized as adding 2 to itself once: \[2 + 2 = 4\]
You perform this operation to simplify the expression and get a single numerical answer, which in this case is 4.

• Remember, multiplication is a common operation in algebra.
• It helps combine terms and simplify expressions.

Understanding multiplication well enables you to tackle increasingly complex problems as they arise in algebra and beyond.

Algebraic Expressions

An algebraic expression is a mathematical phrase involving numbers, variables, and operation signs. It doesn't have an equality sign like equations do. Algebraic expressions can include a range of terms, operations, and variables.

In our initial exercise, the expression is \((x)(x)\). This expression indicates that a variable "x" is being multiplied by itself. These expressions allow us to represent relationships and changes effectively.

Recognizing and working with algebraic expressions involves:

• Identifying variables and constants.
• Applying operations such as addition, subtraction, and in our case, multiplication.
• Making substitutions when necessary to evaluate or simplify the expression.

Understanding how to handle algebraic expressions equips you with a strong foundation in algebra, preparing you for more challenging mathematical problems.