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Chapter 0: Problem 102

Find the value of each expression if \(x=2\) and \(y=-1\) \((x+y)^{2}\)

Short Answer

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Step by step solution

01

- Substitute values for x and y

Replace x with 2 and y with -1 in the expression \( (x + y)^2 \). This gives \( ((2) + (-1))^2 \).
02

- Simplify inside the parentheses

Add the numbers inside the parentheses: \( 2 + (-1) = 1 \). So the expression becomes \( (1)^2 \).
03

- Calculate the square

Find the square of 1: \( 1^2 = 1 \).

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Key Concepts

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

substitution_in_algebra
Substitution in algebra involves replacing variables with specific values. This helps us to evaluate expressions.
In our exercise, we're given that \( x = 2 \) and \( y = -1 \).
We substitute these values into the expression \( (x + y)^2 \).
So, we replace \( x \) with 2 and \( y \) with -1.
This process gives us the expression: \( (2 + (-1))^2 \).
Substitution makes it easier to turn algebraic expressions into numerical ones that we can solve.
It's a foundational skill in algebra.
Get comfortable with it, and you鈥檒l find more complex problems much easier to handle.
simplifying_expressions
Simplifying expressions is about making them easier to understand or solve. After substitution, we often need to simplify the expression further.
In our problem, post-substitution, we have \( (2 + (-1))^2 \).
First, we handle the operation inside the parentheses: \( 2 + (-1) \).
Remember that adding a negative is the same as subtracting.
So, \( 2 + (-1) \) simplifies to 1.
The simplified expression is now \( (1)^2 \).
Breaking down problems step-by-step like this makes tackling algebra much smoother.
squaring_numbers
Squaring numbers means multiplying a number by itself.
It's an important operation in algebra and appears frequently in various contexts.
In the given exercise, our simplified expression was \( (1)^2 \).
To square 1, we multiply it by itself: \( 1 \times 1 \), which equals 1.
Remember, squaring can affect how we understand and solve problems.
Another example could be squaring 2. \( 2^2 \) equals 4 because \( 2 \times 2 = 4 \).
Understanding how to square numbers helps in solving many algebraic problems efficiently.

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Most popular questions from this chapter

Use a calculator to approximate each radical. Round your answer to two decimal places. $$\frac{3 \sqrt[3]{5}-\sqrt{2}}{\sqrt{3}}$$

Simplify each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive. $$\frac{\left(x^{2} y\right)^{1 / 3}\left(x y^{2}\right)^{2 / 3}}{x^{2 / 3} y^{2 / 3}}$$

Expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. $$6(6 x+1)^{1 / 3}(4 x-3)^{3 / 2}+6(6 x+1)^{4 / 3}(4 x-3)^{1 / 2} \quad x \geq \frac{3}{4}$$

Expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. $$\left(x^{2}+4\right)^{4 / 3}+x \cdot \frac{4}{3}\left(x^{2}+4\right)^{1 / 3} \cdot 2 x$$

Rationalize the denominator of each expression. Assume that all variables are positive when they appear. $$\frac{\sqrt{3}-1}{2 \sqrt{3}+3}$$
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