### Chap 6: Anything Wrong?

Antonio, Benedict and Celine were tasked to factorise the following:
40ax - 10bx - 60ay + 15by
and all three presented different answers.

Antonio. (10x - 15y)(4a - b)
Benedict. (2x - 3y)(20a - 5b)
Celine. 5(3y - 2x)(b - 4a)

Discuss the solution by each student and determine if each is correct.
- if the answer is correct, describe how he/ she arrived at that answer
- if the answer is incomplete, how should he/she continue from there
- if the answer is incorrect, point out what is the likely mistake

1. Antonio

40ax-10bx-60ay+15by
=10x(4a-b)-15y(4a-b)
=(10x-15y)(4a-b)

1. The response is incomplete.
Refer to the 3 bullet points to guide your explanation for each student's response.

2. antonio is correct while benedict is wrong, celine can be simplified more
antonio working:40ax-10bx-60ay+15by
=10x(4a-b)-15y(4a-b)
=(10x-15y)(4a-b)
benedict is wrong as he should not times 5 to (4a-b)
celine can simplify more further by having (3y - 2x) times 5

1. Perp perhaps you can work out your answers and make a comparison with the three answers?
That might help to explain the differences.

3. Antonio has an incomplete answer. He should factorise (10x-15y) to 5(2x-3y)

Benedict has an incomplete answer. He should factorise (20a-5b) to 5(4a-b)

40ax-10bx-60ay+15by=10x(4a-b)-15y(4a-b)
=(10x-15y)(4a-b)
=5(2x-3y)(4a-b)

1. Good explanation for Antonio and Benedict's answers.
For Celine's, look at her answer and yours (last line). Compare. Do you see any difference?

4. Cerline is correct. Antonio's answer is wrong because he did not further factorise (10x-15y) to 5(2x-3y). Benedict's answer is wrong because he also did not further factorise (20a-5b) to 5(4a-b).

Cerline is right. She arrived at the answer by doing the following steps:

40ax-10bx-60ay+15by = 20a(2x-3y)-5b(2x-3y)

= (2x-3y)(20a-5b)

= (2x-3y)5(4a-b)

= 5(2x-3y)(4a-b)

1. From your description, both Antonio and Benedict are not wrong. But their factorization is incomplete.
As of your final answer and Celine's. Compare. Do they look the same? Is here still correct?

5. Cerline is the only one who further factorised further thus she is correct.

6. Antonio is Correct
My Working :
40ax - 10bx - 60ay + 15by
= 10x (4a - b)- 15y (4a - b)
= (4a - b) (10x - 15y)

Benedict is wrong as he should not times 5 to (4a-b)
Celine can simplify more further.