Question
Which expressions are equivalent to the expression (x-y)5/8-1/4x+y
?
Select each correct answer.
A
38x+38y\frac{3}{8}x+\frac{3}{8}y
8
3
x+
8
3
y
B
38x+158y\frac{3}{8}x+1\frac{5}{8}y
8
3
x+1
8
5
y
C
58x−y−14x+y\frac{5}{8}x-y-\frac{1}{4}x+y
8
5
x−y−
4
1
x+y
D
58x−58y−14x+y\frac{5}{8}x-\frac{5}{8}y-\frac{1}{4}x+y\newline
8
5
x−
8
5
y−
4
1
x+y
E
58x−14x+y−58y\frac{5}{8}x-\frac{1}{4}x+y-\frac{5}{8}y
8
5
x−
4
1
x+y−
8
5
y
?
Select each correct answer.
A
38x+38y\frac{3}{8}x+\frac{3}{8}y
8
3
x+
8
3
y
B
38x+158y\frac{3}{8}x+1\frac{5}{8}y
8
3
x+1
8
5
y
C
58x−y−14x+y\frac{5}{8}x-y-\frac{1}{4}x+y
8
5
x−y−
4
1
x+y
D
58x−58y−14x+y\frac{5}{8}x-\frac{5}{8}y-\frac{1}{4}x+y\newline
8
5
x−
8
5
y−
4
1
x+y
E
58x−14x+y−58y\frac{5}{8}x-\frac{1}{4}x+y-\frac{5}{8}y
8
5
x−
4
1
x+y−
8
5
y
Answers
GPT-4o mini
To find which expressions are equivalent to \((x - y)^{\frac{5}{8}} - \frac{1}{4}x + y\), we need to analyze each option and see if they can be transformed to match the original expression.
1. **Original expression**:
\[ (x - y)^{\frac{5}{8}} - \frac{1}{4}x + y \]
2. **Checking each option**:
- **Option A**:
\[ \frac{3}{8}x + \frac{3}{8}y \]
This does not resemble the structure of the original expression.
- **Option B**:
\[ \frac{3}{8}x + 1\frac{5}{8}y = \frac{3}{8}x + \frac{13}{8}y \]
Does not match the structure.
- **Option C**:
\[ \frac{5}{8}x - y - 1\frac{4}{1}x + y = \frac{5}{8}x - y - \frac{1}{4}x + y \]
Combining terms, this terms do not simplify to match the original form.
- **Option D**:
\[ \frac{5}{8}x - \frac{5}{8}y - 1\frac{4}{1}x + y = \frac{5}{8}x - \frac{1}{4}x + y - \frac{5}{8}y \]
This simplifies incorrectly.
- **Option E**:
\[ \frac{5}{8}x - 1\frac{4}{1}x + y - \frac{5}{8}y = \frac{5}{8}x - \frac{1}{4}x + y - \frac{5}{8}y \]
After several attempts, this does not correlate correctly either.
From brief checks, none of the options provide equivalence to the original expression. Further algebraic manipulation may be needed to establish if any transformations yield an equivalent value.
Conclusively, without real-time calculations, none of these expressions effectively yield \((x - y)^{\frac{5}{8}} - \frac{1}{4}x + y\). The original expression is unusual due to power and mixed variables which may mislead early calculations. Please confirm whether original equality setups or variable replacements were properly followed in evolving into this format.
1. **Original expression**:
\[ (x - y)^{\frac{5}{8}} - \frac{1}{4}x + y \]
2. **Checking each option**:
- **Option A**:
\[ \frac{3}{8}x + \frac{3}{8}y \]
This does not resemble the structure of the original expression.
- **Option B**:
\[ \frac{3}{8}x + 1\frac{5}{8}y = \frac{3}{8}x + \frac{13}{8}y \]
Does not match the structure.
- **Option C**:
\[ \frac{5}{8}x - y - 1\frac{4}{1}x + y = \frac{5}{8}x - y - \frac{1}{4}x + y \]
Combining terms, this terms do not simplify to match the original form.
- **Option D**:
\[ \frac{5}{8}x - \frac{5}{8}y - 1\frac{4}{1}x + y = \frac{5}{8}x - \frac{1}{4}x + y - \frac{5}{8}y \]
This simplifies incorrectly.
- **Option E**:
\[ \frac{5}{8}x - 1\frac{4}{1}x + y - \frac{5}{8}y = \frac{5}{8}x - \frac{1}{4}x + y - \frac{5}{8}y \]
After several attempts, this does not correlate correctly either.
From brief checks, none of the options provide equivalence to the original expression. Further algebraic manipulation may be needed to establish if any transformations yield an equivalent value.
Conclusively, without real-time calculations, none of these expressions effectively yield \((x - y)^{\frac{5}{8}} - \frac{1}{4}x + y\). The original expression is unusual due to power and mixed variables which may mislead early calculations. Please confirm whether original equality setups or variable replacements were properly followed in evolving into this format.