Question

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

Short answer

1

Step-by-step solution

- Substitute values for x and y

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

- Simplify inside the parentheses

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

- Calculate the square

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

Key concepts

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’ll 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.