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Factorise 6xy – 4y + 6 – 9x.
- a)(3x – 2) (2y – 3)
- b)(3x – 2)
- c)(2y – 3)
- d)(2x – 3) (3y – 2)
Correct answer is option 'A'. Can you explain this answer?
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Factorise 6xy – 4y + 6 – 9x.a)(3x – 2) (2y – 3...
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Factorise 6xy – 4y + 6 – 9x.a)(3x – 2) (2y – 3...
Understanding the Expression
To factorise the expression 6xy – 4y + 6 – 9x, we first rearrange it for clarity:
- Rearranged expression: 6xy - 9x - 4y + 6
Grouping Terms
Next, we will group the terms:
- Group 1: (6xy - 9x)
- Group 2: (-4y + 6)
Factoring Each Group
Now, we will factor out the common factors from each group:
- From Group 1 (6xy - 9x):
- Common factor: 3x
- Factored form: 3x(2y - 3)
- From Group 2 (-4y + 6):
- Common factor: -2
- Factored form: -2(2y - 3)
Combining the Factored Groups
Now, we combine the factored forms:
- 3x(2y - 3) - 2(2y - 3)
Notice that (2y - 3) is a common factor.
Final Factoring
We can factor out (2y - 3):
- Final expression: (2y - 3)(3x - 2)
Thus, the factored form of the original expression is:
- (3x - 2)(2y - 3)
Conclusion
The correct answer is option 'A':
- (3x - 2)(2y - 3)
This demonstrates how to factorise the expression step by step.
To factorise the expression 6xy – 4y + 6 – 9x, we first rearrange it for clarity:
- Rearranged expression: 6xy - 9x - 4y + 6
Grouping Terms
Next, we will group the terms:
- Group 1: (6xy - 9x)
- Group 2: (-4y + 6)
Factoring Each Group
Now, we will factor out the common factors from each group:
- From Group 1 (6xy - 9x):
- Common factor: 3x
- Factored form: 3x(2y - 3)
- From Group 2 (-4y + 6):
- Common factor: -2
- Factored form: -2(2y - 3)
Combining the Factored Groups
Now, we combine the factored forms:
- 3x(2y - 3) - 2(2y - 3)
Notice that (2y - 3) is a common factor.
Final Factoring
We can factor out (2y - 3):
- Final expression: (2y - 3)(3x - 2)
Thus, the factored form of the original expression is:
- (3x - 2)(2y - 3)
Conclusion
The correct answer is option 'A':
- (3x - 2)(2y - 3)
This demonstrates how to factorise the expression step by step.
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