Problem 88 - Algebra 1

Question

Evaluate the expression. -y^{2} \text { when } y=-1

Step-by-Step Solution

Answer

-1

Step 1: Substitute the value of y

In the given expression -y^{2}, substitute the value of y i.e., replace y with -1. So the expression becomes -(-1)^{2}.

Step 2: Simplify the expression

Simplify the expression -(-1)^{2} by first squaring the -1 in the bracket and then applying the negative sign. Squaring -1 gives 1 and applying the negative sign makes it -1. Hence, the expression simplifies to -1.

Key Concepts

Evaluating Expressions

In algebra, evaluating expressions involves simplifying an expression by substituting its variables with given numbers. This helps to determine the expression's value. When working with algebraic expressions:

• Identify the variables.
• Determine the values of these variables, usually provided in the problem.
• Replace the variables with their respective values.
• Use the order of operations (PEMDAS/BODMAS) to simplify the expression to a single number.

Evaluating expressions accurately requires attention to detail, especially when dealing with negative numbers or exponents. By following these steps, you can simplify expressions confidently and effectively.

Substitution Method

Substitution is a fundamental technique in algebra that allows us to solve or evaluate expressions. Let's take a closer look at how it works:This method involves replacing a variable in an expression with a specific value.

• Begin by identifying which variable you need to substitute. In our example, the variable is \( y \).
• Determine the value you will substitute. Here, \( y = -1 \).
• Substitute the variable with the given value in the expression. Hence, the expression \( -y^2 \) becomes \( -(-1)^2 \).

Substitution is particularly useful when working with formulae and expressions involving more than one variable. It helps to break down the problem into simpler parts that can be managed more easily.

Squaring Negative Numbers

Understanding how to square negative numbers is crucial in algebra, as it often comes into play when working with expressions and equations. Here's how it works:When you square a number, you multiply it by itself. This is straightforward with positive numbers, but negative numbers can seem tricky.

• If the negative sign is inside the parenthesis, such as \((-1)^2\), you square the number including the negative sign, which results in a positive product: \((-1) \times (-1) = 1\).
• However, if you apply the square after a negative sign, like in our example \(-(-1)^2\), first square the number ignoring the negative sign outside of it: \((-1) \times (-1) = 1\), then apply the negative sign, resulting in \(-1\).

Remember that squaring negative numbers turns them positive when done inside parentheses, but be aware of additional negative signs that might alter the final result.