Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( (3a - 1)(x + y) \)
Solution
To factorize the expression \( 3 a x + 3 a y - x - y \) fully, follow these steps:
1. **Group like terms:**
\[
3 a x + 3 a y - x - y = (3 a x - x) + (3 a y - y)
\]
2. **Factor out the common terms in each group:**
\[
x(3a - 1) + y(3a - 1)
\]
3. **Factor out the common binomial factor \((3a - 1)\):**
\[
(3a - 1)(x + y)
\]
**Final Factored Form:**
\[
(3a - 1)(x + y)
\]
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Simplify this solution The Deep Dive
To factorise the expression \( 3ax + 3ay - x - y \), we can group the terms effectively. Start by grouping the first two terms and the last two terms: \[ (3ax + 3ay) - (x + y) \] Now, we can factor out common factors from each group. From the first group, we can factor out \( 3a \), and from the second group, we can factor out \( 1 \): \[ 3a(x + y) - 1(x + y) \] Now, we see that \( (x + y) \) is a common factor, so we can factor that out: \[ (x + y)(3a - 1) \] Thus, the fully factorised form of the expression is: \[ (x + y)(3a - 1) \]
