Problem 87 Evaluate each expression when \(... [FREE SOLUTION]

Chapter 1: Problem 87

Evaluate each expression when $x=9$ and $y=-2 .$ See Example 12 $$ -3 y^{2} $$

Short Answer

Expert verified

The expression evaluates to -12.

Step by step solution

Substitute the Value of y

First, we need to substitute the value of $ y = -2 $ into the expression $ -3 y^{2} $. This gives us $ -3(-2)^{2} $.

Calculate y squared

Square the value of $ y $. We have $ (-2)^{2} = 4 $.

Multiply by -3

Now multiply the result by -3: $ -3 \times 4 = -12 $.

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Key Concepts

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

Substituting Values

In algebra, substituting values is a key step to evaluate expressions. This simply means replacing the variables in an expression with the provided numerical values. Let's say you have an expression with variables, such as $-3y^2$, and you're given $y = -2$. Your job is to "substitute" $-2$ wherever you see $y$ in the expression. This process transforms our expression into $-3(-2)^2$.

Identify the variable(s) in the expression.
Replace each variable with its given value.
Ensure all substitutions respect the original expression's structure.

This step prepares the expression for further operations like squaring and multiplication. It sets the stage for a dry run through the exact calculations, one step at a time.

Squaring Numbers

Squaring a number involves multiplying the number by itself. This is a straightforward yet crucial step in algebra, as it often comes up in various expressions and equations. In our problem, after substituting $y$ with $-2$, we encounter $(-2)^2$.

Understand that squaring $-2$ means computing $(-2) \times (-2)$.
Remind yourself that multiplying two negative numbers results in a positive number.
Therefore, $(-2)^2 = 4$.

It's important to work out the square carefully to avoid errors in further calculations. Squaring affects the sign and magnitude of numbers, which impacts every subsequent arithmetic operation.

Multiplication in Algebra

Multiplication in algebra means taking two numbers or expressions and finding their product. In our initial expression, once we've squared $y$ to get $4$, we multiply this result by $-3$. The expression will be $-3 \times 4$.

Recall that multiplying a negative number by a positive one gives a negative result.
Perform the multiplication: $-3 \times 4 = -12$.
This final result is the value of the expression $-3y^2$ when $y = -2$.

Multiplication can change the number's sign, depending on whether the numbers being multiplied are positive or negative, making it a fundamental operation to master when dealing with algebraic expressions.

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91影视

Evaluate each expression when \(x=9\) and \(y=-2 .\) See Example 12 $$ -3 y^{2} $$

Short Answer

Step by step solution

Substitute the Value of y

Calculate y squared

Multiply by -3

Key Concepts

Substituting Values

Squaring Numbers

Multiplication in Algebra

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