subtract by horizontal arrangemen (a) \( 3 x+y-z \) from \( x-4 y+3 z \)

To subtract the expression \( 3x + y - z \) from \( x - 4y + 3z \), we can line them up horizontally and perform the subtraction term by term: Starting with \( x - 4y + 3z \) and subtracting \( 3x + y - z \), it looks like this: \[ (x - 3x) + (-4y - y) + (3z + z) = -2x - 5y + 4z. \] The result of the subtraction is \( -2x - 5y + 4z \). Now let’s visualize this. Imagine you're in a friendly math competition at a carnival. You have two big signs, one with the first expression and another with the second. You start by removing the “stuff” (terms) you don’t want, leaving behind a colorful array of what you need! Math can be quite the show, turning tedious into a fun challenge! Also, try to remember common mistakes like forgetting to change the signs of the second expression during the subtraction step! It's like taking away prizes but accidentally gifting some back. Double-check your signs, and you'll have a better chance of winning that math game. Enjoy playing with expressions!