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Find the remainder when [tex]$(a-b)^3$[/tex] is subtracted from [tex]$(a+b)$[/tex].

Sagot :

GinnyAnsweridn
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].
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