Answered

Expand your knowledge base with the help of IDNLearn.com's extensive answer archive. Get the information you need from our community of experts who provide accurate and thorough answers to all your questions.

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].
We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. IDNLearn.com provides the best answers to your questions. Thank you for visiting, and come back soon for more helpful information.