%5E2.jpeg "(-x-1)^2")
Understanding (-x-1)^2
This expression involves squaring a binomial, which is a sum or difference of two terms. Let's break it down and understand how to simplify it.
Expanding the Expression
The expression (-x-1)^2 means multiplying the binomial (-x-1) by itself.
(-x-1)^2 = (-x-1) * (-x-1)
To simplify, we need to apply the distributive property (also known as FOIL method).
FOIL stands for:
- First: Multiply the first terms of each binomial.
- Outer: Multiply the outer terms of the binomials.
- Inner: Multiply the inner terms of the binomials.
- Last: Multiply the last terms of each binomial.
Applying FOIL to our expression:
- First: (-x) * (-x) = x^2
- Outer: (-x) * (-1) = x
- Inner: (-1) * (-x) = x
- Last: (-1) * (-1) = 1
Now, combine the terms:
x^2 + x + x + 1
Simplifying the Expression
Finally, combine the like terms:
x^2 + 2x + 1
Therefore, the simplified form of (-x-1)^2 is x^2 + 2x + 1.
Key Points to Remember
- Remember that squaring a binomial involves multiplying it by itself.
- The FOIL method helps to systematically expand the expression.
- Combine like terms to get the simplified form.
This understanding of expanding and simplifying binomials is essential in various mathematical contexts, including algebra, calculus, and more.