William multiplied (-2x+1-3y)(-0.5x) and got the wrong solution. Review his work and identify the step in which William made his first error.
Step 1 (-2x+1-3y)(-0.5x)
Step 2 (-0.5x)(-2x-3y+1)
Step 3 -0.5x(-2x)-0.5x(-3y)-0.5x(1)
Step 4 x^2+1.5xy-x
I think it’s step 4 but I’m getting a different answer please shoe me which step and how to find solution
step 4: -0.5x(1) ≠ -x
Let's go through each step and identify where the first error occurred.
Step 1: (-2x+1-3y)(-0.5x)
This step appears to be correct. The expression (-2x+1-3y) is multiplied by (-0.5x).
Step 2: (-0.5x)(-2x-3y+1)
Again, this step seems fine. The expression (-0.5x) is multiplied by the terms (-2x-3y+1).
Step 3: -0.5x(-2x)-0.5x(-3y)-0.5x(1)
Here, William distributes -0.5x to each term inside the parentheses. This is also done correctly.
Step 4: x^2+1.5xy-x
However, this is where the first error occurred. Let's examine the steps to see what went wrong.
To simplify the expression in Step 3 correctly, we need to distribute -0.5x to each term:
-0.5x(-2x) = -0.5x * -2x = x^2
-0.5x(-3y) = -0.5x * -3y = 1.5xy
-0.5x(1) = -0.5x * 1 = -0.5x
Hence, the correct result after simplification should be:
x^2 + 1.5xy - 0.5x
So William's error was mistakenly subtracting x instead of subtracting 0.5x in Step 4.
To get the correct solution, follow the correct simplification process from Step 3:
-0.5x(-2x) = x^2
-0.5x(-3y) = 1.5xy
-0.5x(1) = -0.5x
Combining these terms gives the correct solution:
x^2 + 1.5xy - 0.5x