2-in-the-expanded-form-is.jpeg "(2x-y+z)2 In The Expanded Form Is")
Expanding (2x - y + z)^2
This expression represents the square of a trinomial, meaning it's the product of the trinomial multiplied by itself:
(2x - y + z)^2 = (2x - y + z)(2x - y + z)
To expand this, we can use the distributive property (also known as FOIL for binomials) multiple times. Let's break it down:
1. Distribute the first term (2x):
(2x - y + z)(2x - y + z) = 2x(2x - y + z) - y(2x - y + z) + z(2x - y + z)
2. Distribute the remaining terms (-y and z):
= 4x^2 - 2xy + 2xz - 2xy + y^2 - yz + 2xz - yz + z^2
3. Combine like terms:
= 4x^2 - 4xy + 4xz + y^2 - 2yz + z^2
Therefore, the expanded form of (2x - y + z)^2 is 4x^2 - 4xy + 4xz + y^2 - 2yz + z^2.
Important Note: Remember that squaring a trinomial is not simply squaring each individual term. The expansion involves the product of all possible pairs of terms within the trinomial.