Solve (x+y-z)(2x-y): Multiplying Two Algebraic Expressions

To expand and solve the expression $(x+y-z) \cdot (2x-y)$, follow these steps:

Step 1: Apply the distributive property to the expression.
We distribute each term in $(x+y-z)$ to each term in $(2x-y)$.

Step 2: Calculate the products:
- First, distribute $x$ to both $2x$ and $-y$:

• $x \cdot 2x = 2x^2$
• $x \cdot (-y) = -xy$

- Next, distribute $y$ to both $2x$ and $-y$:

• $y \cdot 2x = 2xy$
• $y \cdot (-y) = -y^2$

- Finally, distribute $-z$ to both $2x$ and $-y$:

• $-z \cdot 2x = -2xz$
• $-z \cdot (-y) = yz$

Step 3: Combine all the terms from the above calculations:
$2x^2 - xy + 2xy - y^2 - 2xz + yz$.

Step 4: Simplify by combining like terms:
- Combine $-xy$ and $2xy$ to get $xy$.

Therefore, the expanded expression is:
$2x^2 + xy - y^2 - 2xz + yz$.

This corresponds to choice $1$.

Hence, the correct expanded expression is $2x^2 + xy - y^2 - 2xz + yz$.