Understanding the Expression
To factorise the expression 12xy - 6x + 4y - 2, we will group the terms and look for common factors.
Step 1: Grouping Terms
- We can group the expression into two parts:
- (12xy - 6x)
- (4y - 2)
Step 2: Factoring Each Group
- For the first group (12xy - 6x):
- The common factor is 6x.
- Factoring out 6x gives:
- 6x(2y - 1)
- For the second group (4y - 2):
- The common factor is 2.
- Factoring out 2 gives:
- 2(2y - 1)
Step 3: Combining the Factors
- Now we can combine the factored groups:
- We have:
- 6x(2y - 1) + 2(2y - 1)
Step 4: Final Factoring
- Notice that (2y - 1) is a common factor in both terms:
- Factoring out (2y - 1) gives:
- (2y - 1)(6x + 2)
Step 5: Simplifying Further
- The second part, (6x + 2), can be simplified:
- It has a common factor of 2.
- Factoring out 2 gives:
- 2(3x + 1)
Final Factorized Form
- Thus, the fully factorized expression is:
- 2(2y - 1)(3x + 1)
Conclusion
- The expression 12xy - 6x + 4y - 2 can be factorized as:
- 2(2y - 1)(3x + 1).
This systematic approach helps in understanding the process of factoring polynomials effectively!