Question
if a, b, and c are constants, is a(x - b) - c + ax - (ab + c)? explain
Answers
GPT-4o mini
Let's simplify the expression \( a(x - b) - c + ax - (ab + c) \) step by step to see if it equals zero or if we can further simplify it.
1. **Distribute** \( a \) in the term \( a(x - b) \):
\[
a(x - b) = ax - ab
\]
2. **Rewrite the expression with this substitution**:
\[
ax - ab - c + ax - (ab + c)
\]
3. **Simplify the expression**:
Combine like terms:
- The terms \( ax \) and \( ax \) combine to \( 2ax \).
- The constants \( -ab \) and \( -ab \) combine to \( -2ab \).
- The constants \( -c \) and \( -c \) combine to \( -2c \).
So, we have:
\[
2ax - 2ab - 2c
\]
4. **Factor out common terms**:
We can factor out a 2:
\[
2(ax - ab - c)
\]
So, the expression \( a(x - b) - c + ax - (ab + c) \) simplifies to \( 2(ax - ab - c) \).
### Conclusion
The expression is not always equal to zero. It simplifies to \( 2(ax - ab - c) \). Whether this expression is zero or not depends on the specific values of \( a \), \( b \), \( c \), and \( x \).
1. **Distribute** \( a \) in the term \( a(x - b) \):
\[
a(x - b) = ax - ab
\]
2. **Rewrite the expression with this substitution**:
\[
ax - ab - c + ax - (ab + c)
\]
3. **Simplify the expression**:
Combine like terms:
- The terms \( ax \) and \( ax \) combine to \( 2ax \).
- The constants \( -ab \) and \( -ab \) combine to \( -2ab \).
- The constants \( -c \) and \( -c \) combine to \( -2c \).
So, we have:
\[
2ax - 2ab - 2c
\]
4. **Factor out common terms**:
We can factor out a 2:
\[
2(ax - ab - c)
\]
So, the expression \( a(x - b) - c + ax - (ab + c) \) simplifies to \( 2(ax - ab - c) \).
### Conclusion
The expression is not always equal to zero. It simplifies to \( 2(ax - ab - c) \). Whether this expression is zero or not depends on the specific values of \( a \), \( b \), \( c \), and \( x \).