Answer :
Let's work through the problem step-by-step to find which expressions are equivalent to [tex]\( 4(-8s + 3) + 4s \)[/tex].
1. Simplify the expression [tex]\( 4(-8s + 3) + 4s \)[/tex]:
- First, distribute the 4 inside the parenthesis:
[tex]\[
4(-8s + 3) = 4 \times -8s + 4 \times 3 = -32s + 12
\][/tex]
- Now, add [tex]\( 4s \)[/tex] to the result:
[tex]\[
-32s + 12 + 4s = -32s + 4s + 12 = -28s + 12
\][/tex]
So, the simplified expression is [tex]\( -28s + 12 \)[/tex].
2. Compare this with each given expression:
a) [tex]\(-8(3s + 4) + 4s\)[/tex]:
- Distribute [tex]\(-8\)[/tex]:
[tex]\[
-8 \times 3s + (-8) \times 4 = -24s - 32
\][/tex]
- Add [tex]\( 4s \)[/tex]:
[tex]\[
-24s - 32 + 4s = -24s + 4s - 32 = -20s - 32
\][/tex]
- [tex]\(-20s - 32\)[/tex] is not equal to [tex]\(-28s + 12\)[/tex].
b) [tex]\(3(-8s + 4) + 4s\)[/tex]:
- Distribute [tex]\(3\)[/tex]:
[tex]\[
3 \times -8s + 3 \times 4 = -24s + 12
\][/tex]
- Add [tex]\( 4s \)[/tex]:
[tex]\[
-24s + 12 + 4s = -24s + 4s + 12 = -20s + 12
\][/tex]
- [tex]\(-20s + 12\)[/tex] is not equal to [tex]\(-28s + 12\)[/tex].
c) [tex]\(-28s + 12\)[/tex]:
- This is already in the simplified form, and it matches exactly [tex]\(-28s + 12\)[/tex].
d) [tex]\(4(3s - 8) + 4s\)[/tex]:
- Distribute [tex]\(4\)[/tex]:
[tex]\[
4 \times 3s + 4 \times -8 = 12s - 32
\][/tex]
- Add [tex]\( 4s \)[/tex]:
[tex]\[
12s - 32 + 4s = 12s + 4s - 32 = 16s - 32
\][/tex]
- [tex]\(16s - 32\)[/tex] is not equal to [tex]\(-28s + 12\)[/tex].
Thus, the expression that is equivalent to [tex]\( 4(-8s + 3) + 4s \)[/tex] is option c) [tex]\(-28s + 12\)[/tex].
1. Simplify the expression [tex]\( 4(-8s + 3) + 4s \)[/tex]:
- First, distribute the 4 inside the parenthesis:
[tex]\[
4(-8s + 3) = 4 \times -8s + 4 \times 3 = -32s + 12
\][/tex]
- Now, add [tex]\( 4s \)[/tex] to the result:
[tex]\[
-32s + 12 + 4s = -32s + 4s + 12 = -28s + 12
\][/tex]
So, the simplified expression is [tex]\( -28s + 12 \)[/tex].
2. Compare this with each given expression:
a) [tex]\(-8(3s + 4) + 4s\)[/tex]:
- Distribute [tex]\(-8\)[/tex]:
[tex]\[
-8 \times 3s + (-8) \times 4 = -24s - 32
\][/tex]
- Add [tex]\( 4s \)[/tex]:
[tex]\[
-24s - 32 + 4s = -24s + 4s - 32 = -20s - 32
\][/tex]
- [tex]\(-20s - 32\)[/tex] is not equal to [tex]\(-28s + 12\)[/tex].
b) [tex]\(3(-8s + 4) + 4s\)[/tex]:
- Distribute [tex]\(3\)[/tex]:
[tex]\[
3 \times -8s + 3 \times 4 = -24s + 12
\][/tex]
- Add [tex]\( 4s \)[/tex]:
[tex]\[
-24s + 12 + 4s = -24s + 4s + 12 = -20s + 12
\][/tex]
- [tex]\(-20s + 12\)[/tex] is not equal to [tex]\(-28s + 12\)[/tex].
c) [tex]\(-28s + 12\)[/tex]:
- This is already in the simplified form, and it matches exactly [tex]\(-28s + 12\)[/tex].
d) [tex]\(4(3s - 8) + 4s\)[/tex]:
- Distribute [tex]\(4\)[/tex]:
[tex]\[
4 \times 3s + 4 \times -8 = 12s - 32
\][/tex]
- Add [tex]\( 4s \)[/tex]:
[tex]\[
12s - 32 + 4s = 12s + 4s - 32 = 16s - 32
\][/tex]
- [tex]\(16s - 32\)[/tex] is not equal to [tex]\(-28s + 12\)[/tex].
Thus, the expression that is equivalent to [tex]\( 4(-8s + 3) + 4s \)[/tex] is option c) [tex]\(-28s + 12\)[/tex].
