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\( (a - 1)(b + 1) \)
Solución
To factorize the expression \( a - b + ab - 1 \), follow these steps:
1. **Rearrange the Terms:**
Start by rearranging the terms to group like terms together:
\[
ab + a - b - 1
\]
2. **Factor by Grouping:**
Notice that you can factor out common terms from the first two terms and the last two terms:
\[
a(b + 1) - 1(b + 1)
\]
3. **Factor Out the Common Binomial:**
Both groups contain the common binomial \( (b + 1) \), so factor that out:
\[
(a - 1)(b + 1)
\]
4. **Final Factored Form:**
The expression is now fully factored as:
\[
(a - 1)(b + 1)
\]
**Verification:**
To ensure the factorization is correct, expand the factored form:
\[
(a - 1)(b + 1) = a \cdot b + a \cdot 1 - 1 \cdot b - 1 \cdot 1 = ab + a - b - 1
\]
This matches the original expression, confirming the factorization is accurate.
**Final Answer:**
\[
(a - 1)(\,b + 1\,)
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución The Deep Dive
To factor the expression \( a - b + ab - 1 \), we can rearrange it as \( ab - b + a - 1 \). By grouping terms, we rewrite it as \( b(a - 1) + (a - 1) \). Now, we can factor out the common term \( (a - 1) \): \[ = (a - 1)(b + 1) \] So, the factored form is \( (a - 1)(b + 1) \). Additionally, if we wanted to check our work, we could expand \( (a - 1)(b + 1) \) back out to ensure it returns us to the original expression. This verification can be a handy technique in algebra!
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