Answer :
Let's simplify the expression step by step:
The original expression is: [tex]\((8b - 4r) - (2b - r)\)[/tex].
1. Remove the parentheses:
To do this, distribute the minus sign across the second set of parentheses:
[tex]\((8b - 4r) - 2b + r\)[/tex].
Here, we change [tex]\( (-(2b) + r) \)[/tex] to [tex]\( -2b + r \)[/tex].
2. Combine like terms:
- For the [tex]\(b\)[/tex] terms:
[tex]\[
8b - 2b = 6b
\][/tex]
- For the [tex]\(r\)[/tex] terms:
[tex]\[
-4r + r = -3r
\][/tex]
So, the simplified expression is: [tex]\(6b - 3r\)[/tex].
3. Identify where Clara went wrong:
Clara's result was [tex]\(6b - 5r\)[/tex]. If you compare it to the correct result [tex]\(6b - 3r\)[/tex], you can see that Clara made an error when combining the [tex]\(r\)[/tex] coefficients. She incorrectly calculated [tex]\(-4r + r\)[/tex] as [tex]\(-5r\)[/tex] instead of [tex]\(-3r\)[/tex].
Therefore, the correct explanation is: Clara incorrectly combined the [tex]\(r\)[/tex] coefficients. The correctly simplified expression is [tex]\(6b - 3r\)[/tex].
The original expression is: [tex]\((8b - 4r) - (2b - r)\)[/tex].
1. Remove the parentheses:
To do this, distribute the minus sign across the second set of parentheses:
[tex]\((8b - 4r) - 2b + r\)[/tex].
Here, we change [tex]\( (-(2b) + r) \)[/tex] to [tex]\( -2b + r \)[/tex].
2. Combine like terms:
- For the [tex]\(b\)[/tex] terms:
[tex]\[
8b - 2b = 6b
\][/tex]
- For the [tex]\(r\)[/tex] terms:
[tex]\[
-4r + r = -3r
\][/tex]
So, the simplified expression is: [tex]\(6b - 3r\)[/tex].
3. Identify where Clara went wrong:
Clara's result was [tex]\(6b - 5r\)[/tex]. If you compare it to the correct result [tex]\(6b - 3r\)[/tex], you can see that Clara made an error when combining the [tex]\(r\)[/tex] coefficients. She incorrectly calculated [tex]\(-4r + r\)[/tex] as [tex]\(-5r\)[/tex] instead of [tex]\(-3r\)[/tex].
Therefore, the correct explanation is: Clara incorrectly combined the [tex]\(r\)[/tex] coefficients. The correctly simplified expression is [tex]\(6b - 3r\)[/tex].
