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Factorize: 20x + 30y
- a)5(4x + 6y)
- b)10(2x + 3y)
- c)2(10x + 15y)
- d)All of these
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Factorize: 20x + 30ya)5(4x + 6y)b)10(2x + 3y)c)2(10x + 15y)d)All of th...
Understanding Factorization
To factorize the expression 20x + 30y, we need to find the greatest common factor (GCF) of the terms involved.
Finding the GCF
- The coefficients are 20 and 30.
- The GCF of 20 and 30 is 10.
So, we can factor out 10 from the expression:
Factoring Out 10
- 20x + 30y = 10(2x) + 10(3y) = 10(2x + 3y)
Now, we can also express this in different ways to check for other factors:
Other Factorizations
- Option a: 5(4x + 6y)
- 4x + 6y can be factored further as 2(2x + 3y). Thus, 5(4x + 6y) = 5 * 2(2x + 3y) = 10(2x + 3y).
- Option c: 2(10x + 15y)
- 10x + 15y can also be factored as 5(2x + 3y). Therefore, 2(10x + 15y) = 2 * 5(2x + 3y) = 10(2x + 3y).
Conclusion
All of these options (5(4x + 6y), 10(2x + 3y), and 2(10x + 15y)) simplify to the same expression, 10(2x + 3y). Hence, the correct answer is option D: All of these.
This shows that the expression can be factored in multiple ways, reinforcing the concept of factorization in algebra.
To factorize the expression 20x + 30y, we need to find the greatest common factor (GCF) of the terms involved.
Finding the GCF
- The coefficients are 20 and 30.
- The GCF of 20 and 30 is 10.
So, we can factor out 10 from the expression:
Factoring Out 10
- 20x + 30y = 10(2x) + 10(3y) = 10(2x + 3y)
Now, we can also express this in different ways to check for other factors:
Other Factorizations
- Option a: 5(4x + 6y)
- 4x + 6y can be factored further as 2(2x + 3y). Thus, 5(4x + 6y) = 5 * 2(2x + 3y) = 10(2x + 3y).
- Option c: 2(10x + 15y)
- 10x + 15y can also be factored as 5(2x + 3y). Therefore, 2(10x + 15y) = 2 * 5(2x + 3y) = 10(2x + 3y).
Conclusion
All of these options (5(4x + 6y), 10(2x + 3y), and 2(10x + 15y)) simplify to the same expression, 10(2x + 3y). Hence, the correct answer is option D: All of these.
This shows that the expression can be factored in multiple ways, reinforcing the concept of factorization in algebra.
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Community Answer
Factorize: 20x + 30ya)5(4x + 6y)b)10(2x + 3y)c)2(10x + 15y)d)All of th...
20x + 30y = 10(2x + 3y)
= 5(4x + 6y)
= 2(10x + 15y)
= 5(4x + 6y)
= 2(10x + 15y)
Hence, all are correct.
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