Answer :
Sure, let's work through the problem step by step for both parts:
### Part a: [tex]\(4a + 7b + 5a - b\)[/tex]
1. Combine like terms (terms involving [tex]\(a\)[/tex] and terms involving [tex]\(b\)[/tex]):
- Look at the terms involving [tex]\(a\)[/tex]: [tex]\(4a\)[/tex] and [tex]\(5a\)[/tex].
- Combine them: [tex]\(4a + 5a = 9a\)[/tex].
2. Next, look at the terms involving [tex]\(b\)[/tex]:
- The terms involving [tex]\(b\)[/tex] are [tex]\(7b\)[/tex] and [tex]\(-b\)[/tex].
- Combine them: [tex]\(7b - b = 6b\)[/tex].
3. Combine the results:
- Put together the combined terms involving [tex]\(a\)[/tex] and [tex]\(b\)[/tex]: [tex]\(9a + 6b\)[/tex].
So, [tex]\(4a + 7b + 5a - b = 9a + 6b\)[/tex].
To further simplify using specific values for [tex]\(a\)[/tex] and [tex]\(b\)[/tex], let's assume [tex]\(a = 1\)[/tex] and [tex]\(b = 1\)[/tex]:
[tex]\[ 9a + 6b = 9(1) + 6(1) = 9 + 6 = 15 \][/tex]
### Part b: [tex]\(6c + 4d - c - 7d\)[/tex]
1. Combine like terms (terms involving [tex]\(c\)[/tex] and terms involving [tex]\(d\)[/tex]):
- Look at the terms involving [tex]\(c\)[/tex]: [tex]\(6c\)[/tex] and [tex]\(-c\)[/tex].
- Combine them: [tex]\(6c - c = 5c\)[/tex].
2. Next, look at the terms involving [tex]\(d\)[/tex]:
- The terms involving [tex]\(d\)[/tex] are [tex]\(4d\)[/tex] and [tex]\(-7d\)[/tex].
- Combine them: [tex]\(4d - 7d = -3d\)[/tex].
3. Combine the results:
- Put together the combined terms involving [tex]\(c\)[/tex] and [tex]\(d\)[/tex]: [tex]\(5c - 3d\)[/tex].
So, [tex]\(6c + 4d - c - 7d = 5c - 3d\)[/tex].
To further simplify using specific values for [tex]\(c\)[/tex] and [tex]\(d\)[/tex], let's assume [tex]\(c = 1\)[/tex] and [tex]\(d = 1\)[/tex]:
[tex]\[ 5c - 3d = 5(1) - 3(1) = 5 - 3 = 2 \][/tex]
### Summary
- For part a, [tex]\(4a + 7b + 5a - b = 15\)[/tex] when [tex]\(a = 1\)[/tex] and [tex]\(b = 1\)[/tex].
- For part b, [tex]\(6c + 4d - c - 7d = 2\)[/tex] when [tex]\(c = 1\)[/tex] and [tex]\(d = 1\)[/tex].
So, the final results are:
[tex]\[ \text{Part a: } 15 \][/tex]
[tex]\[ \text{Part b: } 2 \][/tex]
### Part a: [tex]\(4a + 7b + 5a - b\)[/tex]
1. Combine like terms (terms involving [tex]\(a\)[/tex] and terms involving [tex]\(b\)[/tex]):
- Look at the terms involving [tex]\(a\)[/tex]: [tex]\(4a\)[/tex] and [tex]\(5a\)[/tex].
- Combine them: [tex]\(4a + 5a = 9a\)[/tex].
2. Next, look at the terms involving [tex]\(b\)[/tex]:
- The terms involving [tex]\(b\)[/tex] are [tex]\(7b\)[/tex] and [tex]\(-b\)[/tex].
- Combine them: [tex]\(7b - b = 6b\)[/tex].
3. Combine the results:
- Put together the combined terms involving [tex]\(a\)[/tex] and [tex]\(b\)[/tex]: [tex]\(9a + 6b\)[/tex].
So, [tex]\(4a + 7b + 5a - b = 9a + 6b\)[/tex].
To further simplify using specific values for [tex]\(a\)[/tex] and [tex]\(b\)[/tex], let's assume [tex]\(a = 1\)[/tex] and [tex]\(b = 1\)[/tex]:
[tex]\[ 9a + 6b = 9(1) + 6(1) = 9 + 6 = 15 \][/tex]
### Part b: [tex]\(6c + 4d - c - 7d\)[/tex]
1. Combine like terms (terms involving [tex]\(c\)[/tex] and terms involving [tex]\(d\)[/tex]):
- Look at the terms involving [tex]\(c\)[/tex]: [tex]\(6c\)[/tex] and [tex]\(-c\)[/tex].
- Combine them: [tex]\(6c - c = 5c\)[/tex].
2. Next, look at the terms involving [tex]\(d\)[/tex]:
- The terms involving [tex]\(d\)[/tex] are [tex]\(4d\)[/tex] and [tex]\(-7d\)[/tex].
- Combine them: [tex]\(4d - 7d = -3d\)[/tex].
3. Combine the results:
- Put together the combined terms involving [tex]\(c\)[/tex] and [tex]\(d\)[/tex]: [tex]\(5c - 3d\)[/tex].
So, [tex]\(6c + 4d - c - 7d = 5c - 3d\)[/tex].
To further simplify using specific values for [tex]\(c\)[/tex] and [tex]\(d\)[/tex], let's assume [tex]\(c = 1\)[/tex] and [tex]\(d = 1\)[/tex]:
[tex]\[ 5c - 3d = 5(1) - 3(1) = 5 - 3 = 2 \][/tex]
### Summary
- For part a, [tex]\(4a + 7b + 5a - b = 15\)[/tex] when [tex]\(a = 1\)[/tex] and [tex]\(b = 1\)[/tex].
- For part b, [tex]\(6c + 4d - c - 7d = 2\)[/tex] when [tex]\(c = 1\)[/tex] and [tex]\(d = 1\)[/tex].
So, the final results are:
[tex]\[ \text{Part a: } 15 \][/tex]
[tex]\[ \text{Part b: } 2 \][/tex]
