2-in-the-expanded-form-is.jpeg "(2x-y+z)2 In The Expanded Form Is")
Expanding the Expression: (2x-y+z)²
When dealing with algebraic expressions, it's essential to understand how to expand and simplify them. One common expression that students often struggle with is (2x-y+z)². In this article, we'll break down the steps to expand this expression and reveal its expanded form.
The Binomial Theorem
To expand (2x-y+z)², we can use the binomial theorem, which states that for any expression (a+b)², the expanded form is:
(a+b)² = a² + 2ab + b²
In our case, we need to apply this theorem to (2x-y+z)². Let's start by identifying the values of a, b, and c:
a = 2x
b = -y
c = z
Expanding the Expression
Now, we can plug these values into the binomial theorem:
(2x-y+z)² = (2x)² + 2(2x)(-y) + (-y)² + 2(-y)(z) + (z)²
Simplifying each term, we get:
(2x)² = 4x²
2(2x)(-y) = -4xy
(-y)² = y²
2(-y)(z) = -2yz
(z)² = z²
Combining these terms, we finally get the expanded form of (2x-y+z)²:
(2x-y+z)² = 4x² - 4xy + y² - 2yz + z²
And that's it! We've successfully expanded the expression (2x-y+z)² using the binomial theorem.
Conclusion
Expanding algebraic expressions may seem daunting at first, but with the right tools and techniques, it can become a manageable task. By applying the binomial theorem, we were able to break down the expression (2x-y+z)² and reveal its expanded form. Remember to practice expanding different types of expressions to become more comfortable with the process.
