Problem 395 Evaluate each expression. \((x... [FREE SOLUTION]

Chapter 1: Problem 395

Evaluate each expression. \((x+y)^{2}\) when \(x=-3, y=14\)

Short Answer

Expert verified

121

Step by step solution

Substitute the given values

First, substitute the given values for x and y into the expression: Given: \( x = -3 \) \( y = 14 \)Substitute into \((x+y)^{2}\)Thus, \(( -3 + 14 ) ^ {2}\).

Simplify inside the parenthesis

Perform the arithmetic inside the parenthesis:\( -3 + 14 = 11 \)So, the expression simplifies to \( (11)^{2} \)

Square the result

Finally, square the result obtained from step 2:\( 11^{2} = 121 \)

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

substitution

Substitution is a fundamental concept in algebra and mathematics. It involves replacing variables in an expression with their respective values. In this exercise, we start by identifying the values for the variables 'x' and 'y'. Given:

\( x = -3 \)
\( y = 14 \)

We then substitute these values into the given expression \((x+y)^{2}\). This transforms our expression into \((-3 + 14)^2\). Thus, substitution helps us transform an abstract expression into one that can be evaluated numerically.

arithmetic operations

Arithmetic operations are the building blocks of mathematics. These include addition, subtraction, multiplication, and division. In our current problem, we need to perform addition first. According to the problem, after substitution we have the expression \((-3 + 14)^2\).
Here, we perform the operation inside the parenthesis first:

\( -3 + 14 \)

This simple arithmetic operation results in \( 11 \). Thus, arithmetic operations allow us to simplify expressions step by step.

simplifying expressions

Once we perform arithmetic operations, we need to further simplify the expression wherever possible. Simplifying an expression makes it easier to understand and evaluate.
In our exercise, post substitution and arithmetic operations, we have the simplified expression \( 11^2 \). This step-by-step simplification from \((-3 + 14)^2\) to \(11^2\) streamlines our calculations and reduces the complexity of the problem.

squaring numbers

Squaring a number means multiplying it by itself. It is represented as \(a^2\), where \(a\) is any number. In mathematics, squaring is a common operation that often follows simplification.
In our problem, after simplifying the expression to \(11^2\), we now need to square 11.

\( 11^2 = 11 \times 11 = 121 \)

Therefore, \(11^2 = 121\). Squaring helps us reach our final answer by dealing with any remaining exponents in the expression.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Evaluate each expression. \((x+y)^{2}\) when \(x=-3, y=14\)

Short Answer

Step by step solution

Substitute the given values

Simplify inside the parenthesis

Square the result

Key Concepts

substitution

arithmetic operations

simplifying expressions

squaring numbers

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Discrete Mathematics

Applied Mathematics

Calculus

Probability and Statistics

Study anywhere. Anytime. Across all devices.