Factorising

[Sathhin]

Hey, this is one other question I wouldn't mind help with if that's alright

1) Factorise \(\displaystyle 8x^{2}y^{3}z + 2xyz - 4^{3}yz^{2} \)

I ended up with \(\displaystyle 2xyz\left ( 3xy^{2} - 1 + 2x^{2}z \right ) \)

2) Factorise fully into two brackets \(\displaystyle bx - 4y + by - 4x \)

I swapped the terms around and got \(\displaystyle bx + by - 4y - 4x \)
and finished with \(\displaystyle b\left ( x + y \right ) - 4\left ( y - x \right ) \)

Thanks, hoping I can do the rest off my own back

 

[Deleted member 4993]

Hey, this is one other question I wouldn't mind help with if that's alright

1) Factorise \(\displaystyle 8x^{2}y^{3}z + 2xyz - 4^{3}yz^{2} \) I think this should be \(\displaystyle 8x^{2}y^{3}z + 2xyz - 4x^{3}yz^{2} \)

I ended up with \(\displaystyle 2xyz\left ( 3xy^{2} - 1 + 2x^{2}z \right ) \)Incorrect - This should be \(\displaystyle 2xyz\left ( 4xy^{2} - 1 + 2x^{2}z \right ) \)


2) Factorise fully into two brackets \(\displaystyle bx - 4y + by - 4x \)

I swapped the terms around and got \(\displaystyle bx + by - 4y - 4x \) Correct

and finished with \(\displaystyle b\left ( x + y \right ) - 4\left ( y - x \right ) \).... Incorrect

This should be:

b(x + y) - 4 (x + y)

= (x + y)(b - 4)

Thanks, hoping I can do the rest off my own back

We appreciate your showing detailed work.

 

[Sathhin]

Thanks for clearing that up, the first one was me doing typos. Sorry for that, I have the same answer as the one you put, just copied it badly here :/

Not sure I understand the second part. Sorry about being a bit dense here but how does the \(\displaystyle 4y - 4x \) become \(\displaystyle 4\left ( x + y\right ) \), Just curious as to how the negative becomes an addition? Think I'm missing something basic here lol

 

[Deleted member 4993]

Thanks for clearing that up, the first one was me doing typos. Sorry for that, I have the same answer as the one you put, just copied it badly here :/

Not sure I understand the second part. Sorry about being a bit dense here but how does the \(\displaystyle 4y - 4x \) become \(\displaystyle 4\left ( x + y\right ) \), Just curious as to how the negative becomes an addition? Think I'm missing something basic here lol

It is not \(\displaystyle 4y - 4x \) which translates to \(\displaystyle + 4y - 4x \) and then to \(\displaystyle 4(y - x) \)

It is \(\displaystyle - 4y - 4x \) which translates to \(\displaystyle -4 (y + x) \)

 

[Sathhin]

AH! Now I get it, thanks for explaining that