[RESOLVED] Check this question for me, thanks!

[Yunie]

Factorise completely:

16x - 4x + xy - 4y
= 4(4-x) + y(x-4)
= 4(x-4) + y(x-4)
=(x-4)(4+y)

Is this correct? I am not sure as the answer is (4-x)(4-y)

If I am wrong, can please show your workings? Thanks a lot! :)

[opus]

Looks good to me!

[krtxmrtz]

Factorise completely:

16x - 4x + xy - 4y
= 4(4-x) + y(x-4)
= 4(x-4) + y(x-4)
=(x-4)(4+y)

Is this correct? I am not sure as the answer is (4-x)(4-y)

If I am wrong, can please show your workings? Thanks a lot! :)
The second line is wrong:

4(4-x) + y(x-4) = 16 - 4x + xy - 4y and not 16x - 4x + xy - 4y

The third line lacks a minus sign:

4(4-x) + y(x-4) = -4(x-4) + y(x-4)

but this doesn't matter if the second line is already wrong.

[opus]

Damned, I missed that one.
It was before the first coffee (does this excuse count?)

[krtxmrtz]

Damned, I missed that one.
It was before the first coffee (does this excuse count?)
Are you sure it wasn't after the first whisky? :D

I wonder if he mistranscribed it and it really should be
16 - 4x + xy - 4y
in which case the result is
(x - 4)(y - 4)

[Yunie]

Typo error...So sorry guys...Yup, it should be 16 - 4x + xy - 4y :)

So, that means my above answer is still wrong?

By the way, I am a 'she'...

[TheBigB]

(x - 4)(x - 4) is the correct answer.
an easy way to check whether you've factorized correctly, is giving the variables values.
say x = 5 and y = 6
16 - (4 * 5) + (5 * 6) - (4 * 6) = 2
(5-4) * (6-4) = 2
if both output the same value you know the factorization is correct.

[krtxmrtz]

Typo error...So sorry guys...Yup, it should be 16 - 4x + xy - 4y :)

So, that means my above answer is still wrong?

By the way, I am a 'she'...
OK so I made a sex typo :) sorry about that.

According to what I said in post #3,

16 - 4x + xy - 4y
= 4(4-x) + y(x-4)
= -4(x-4) + y(x-4)
=(x-4)(y-4)

[Yunie]

I got it, thanks all! :) :) :)

[Yunie]

OK so I made a sex typo :) sorry about that.

According to what I said in post #3,

16 - 4x + xy - 4y
= 4(4-x) + y(x-4)
= -4(x-4) + y(x-4)
=(x-4)(4-y)


Haha, it's ok, people do make mistakes. :p

Thank you once again. :D

[krtxmrtz]

Have you noticed I corrected the last line? I had made a typo myself.

[Yunie]

Yup, I have noticed that but I thought that the answer could be left as that way so I did not tell you.

[krtxmrtz]

Also, giving values to x and y for a quick check it's a necessary but insufficient condition for your result to be correct, i.e. if the result of giving values is correct, then your algebra is probably correct but you can't be sure. If the result is incorrect then your algebra is definitely wrong.

But you can make the check by working the algebra backwards:

(x-4)(y-4) =
x(y-4) -4(y-4) =
xy -4x -4y + 16

[Yunie]

I see I see...Thank you so much krtxmrtz! :)