In mathematics, it is crucial to understand how different expressions can be equivalent. One common task is simplifying or factoring algebraic expressions to get them into a more manageable form. In this article, we will explore the expression X2 + 2X + 2 and determine which equivalent expression can be derived from it.
Expanding the Given Expression
Before we can determine which expression is equivalent to X2 + 2X + 2, let’s first expand the given expression to see its full form.
X2 + 2X + 2
This expression consists of three terms: X2, 2X, and 2. To expand it, we need to apply the distributive property of multiplication over addition.
X2 + 2X + 2 = X * X + 2 * X + 2
X2 + 2X + 2 = X2 + 2X + 2
So, the expanded form of the given expression is X2 + 2X + 2.
Equivalent Expressions
Now that we have the expanded form of X2 + 2X + 2, let’s explore equivalent expressions that can be derived from it through different operations like factoring or simplifying.
Factoring the Expression
One way to find an equivalent expression is to factor the given expression X2 + 2X + 2. Factoring involves breaking down an expression into its irreducible factors.
Factored form of X2 + 2X + 2:
We need to find two numbers that multiply to 2 (coefficient of the constant term) and add up to 2 (coefficient of the linear term).
Let’s express the term 2 as the product of two numbers: 1 * 2 or -1 * -2.
Trying -1 and -2:
X2 – X – 2X + 2
X(X – 1) – 2(X – 1)
Now, we have a common binomial factor:
(X – 1)(X – 2)
So, the factored form of X2 + 2X + 2 is (X – 1)(X – 2).
Simplifying the Expression
Another way to find an equivalent expression is to simplify the given expression X2 + 2X + 2 by combining like terms or using other algebraic techniques.
Simplified form of X2 + 2X + 2:
In this case, the given expression is already in its simplest form, as there are no like terms that can be combined further.
Therefore, the simplified form of X2 + 2X + 2 remains X2 + 2X + 2.
Conclusion
Understanding how to work with algebraic expressions is fundamental in mathematics. In this article, we explored the expression X2 + 2X + 2 and determined that the equivalent expressions derived from it are (X – 1)(X – 2) through factoring and X2 + 2X + 2 through simplifying.
By practicing factoring and simplifying expressions, you can enhance your algebraic skills and tackle more complex problems with ease. Remember to always check your work to ensure accuracy in your mathematical solutions.
