Absolutely, let's solve the problem step-by-step.
To find the remainder when [tex]\( (a - b)^3 \)[/tex] is subtracted from [tex]\( (a + b) \)[/tex], we need to follow these steps:
1. Calculate [tex]\( a + b \)[/tex]
2. Calculate [tex]\( (a - b)^3 \)[/tex]
3. Subtract [tex]\( (a - b)^3 \)[/tex] from [tex]\( a + b \)[/tex]
Given the values:
- [tex]\( a = 10 \)[/tex]
- [tex]\( b = 5 \)[/tex]
Let's go through each step carefully:
### Step 1: Calculate [tex]\( a + b \)[/tex]
[tex]\[ a + b = 10 + 5 = 15 \][/tex]
### Step 2: Calculate [tex]\( (a - b)^3 \)[/tex]
[tex]\[ a - b = 10 - 5 = 5 \][/tex]
[tex]\[ (a - b)^3 = 5^3 = 125 \][/tex]
### Step 3: Subtract [tex]\( (a - b)^3 \)[/tex] from [tex]\( a + b \)[/tex]
[tex]\[ a + b - (a - b)^3 = 15 - 125 = -110 \][/tex]
### Summary
The values we calculated are:
- [tex]\( a + b = 15 \)[/tex]
- [tex]\( (a - b)^3 = 125 \)[/tex]
- The remainder when [tex]\( (a - b)^3 \)[/tex] is subtracted from [tex]\( a + b \)[/tex] is [tex]\( -110 \)[/tex].
So, the final results are:
- [tex]\( a + b = 15 \)[/tex]
- [tex]\( (a - b)^3 = 125 \)[/tex]
- Remainder [tex]\( = -110 \)[/tex]
Fun fact: The remainder when [tex]\( (a - b)^3 \)[/tex] is subtracted from [tex]\( (a + b) \)[/tex] is [tex]\( -110 \)[/tex].
