Question
Factor by grouping. \[ a b+a c+b+c \] SUBMIT ANSWER
Ask by Page Bryant. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\((b + c)(a + 1)\)
Solution
1. Group the terms into two pairs:
\[
(ab + ac) + (b + c)
\]
2. Factor out the common factor in each group:
\[
a(b+c) + 1(b+c)
\]
3. Now, factor out the common binomial factor \((b+c)\):
\[
(b+c)(a+1)
\]
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Simplify this solution Extra Insights
To factor the expression \( ab + ac + b + c \) by grouping, we can start by rearranging it slightly for clarity: 1. Group the first two terms and the last two terms: \( (ab + ac) + (b + c) \). 2. Factor out the common terms in each group: \( a(b + c) + 1(b + c) \). 3. Now we can factor out the common binomial factor \( (b + c) \): \( (b + c)(a + 1) \). Thus, the factored form of the expression is: \[ (b + c)(a + 1) \]
