Problem 41 Evaluate the given expression fo... [FREE SOLUTION]

91影视

Understanding Elementary Algebra with Geometry

Lewis Hirsch, Arthur Goodman

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 8: Problem 41

Evaluate the given expression for $x=-3$ and $y=5$ $$(x y)^{2}$$

Short Answer

Expert verified

225

Step by step solution

Substitute the values of x and y

First, substitute the given values of the variables into the expression. Here, the values are: $x = -3$ and $y = 5$. Thus, the expression $(x y)^{2}$ becomes $(-3 * 5)^{2}$.

Calculate the product inside the parenthesis

Next, calculate the product of $-3$ and $5$. This gives us $(-3) * 5 = -15$. So, the expression now is $(-15)^{2}$.

Square the result

Finally, square the result obtained in Step 2. Squaring $-15$ gives us $(-15)^{2} = 225$.

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Key Concepts

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

substitution method

The substitution method is a technique used to evaluate algebraic expressions by replacing variables with given values. In our problem, we were given the variables $x$ and $y$ with values $x = -3$ and $y = 5$. The key steps in this method include:

Identifying the variables and their corresponding values.
Replacing each variable in the expression with its value.

By substituting $x = -3$ and $y = 5$ into the expression $(xy)^2$, we simplified the expression to $(-3 * 5)^2$.

algebraic expressions

Algebraic expressions are mathematical phrases that can include numbers, variables, and operation symbols. They do not have an equals sign. In our example, the expression $(xy)^2$ is an algebraic expression where $x$ and $y$ are variables. To evaluate such expressions:

First, substitute the given values of the variables.
Then, perform the arithmetic operations according to the order of operations.

In our problem, once we substituted $x = -3$ and $y = 5$, we multiplied these values to get $-15$, and then squared the result to get $225$.

exponentiation

Exponentiation is a mathematical operation that involves raising a number to the power of another number. In our example, we had to raise $-15$ to the power of 2, denoted as $-15^{2}$. The basic steps for exponentiation include:

Identifying the base ($-15$ in our problem).
Identifying the exponent (2 in our problem).
Multiplying the base by itself as many times as indicated by the exponent.

So, $-15 \times -15 = 225$. Squaring $-15$ resulted in a positive number because a negative number times itself is positive.

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91影视

Evaluate the given expression for \(x=-3\) and \(y=5\) $$(x y)^{2}$$

Short Answer

Step by step solution

Substitute the values of x and y

Calculate the product inside the parenthesis

Square the result

Key Concepts

substitution method

algebraic expressions

exponentiation

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