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

Antonio

ReplyDelete40ax-10bx-60ay+15by

=10x(4a-b)-15y(4a-b)

=(10x-15y)(4a-b)

The response is incomplete.

DeleteRefer to the 3 bullet points to guide your explanation for each student's response.

antonio is correct while benedict is wrong, celine can be simplified more

ReplyDeleteantonio 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

Perp perhaps you can work out your answers and make a comparison with the three answers?

DeleteThat might help to explain the differences.

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

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

Celine has the correct answer. She arrived at the answer by:

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

=(10x-15y)(4a-b)

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

Good explanation for Antonio and Benedict's answers.

DeleteFor Celine's, look at her answer and yours (last line). Compare. Do you see any difference?

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).

ReplyDeleteCerline 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)

From your description, both Antonio and Benedict are not wrong. But their factorization is incomplete.

DeleteAs of your final answer and Celine's. Compare. Do they look the same? Is here still correct?

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

ReplyDeletePlease elaborate

DeleteAntonio is Correct

ReplyDeleteMy 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.

Can you elaborate on your thoughts over Celine's answers?

DeleteCeline is correct . At first she will have the same answer as Antonio but however she further factorized it , thus she is rite .

ReplyDeleteBenedict is wrong as he should not times 5 to ( 4 a -b )

Good if you could show how Celine worked out her answers to aid your explanation.

DeleteCeline is right

ReplyDelete40ax-10bx-60ay+15by

=10x(4a-b) -15y(4a-b)

=(10x-15y)(4a-b)

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

Antonio's working is incomplete as she should factorise it.

Benedict is totally wrong