# Thread: Factorising a complicated expression

1. ## Factorising a complicated expression

factor completely
y^2(x^4-z^4) - x^2(y^4-z^4) +z^2(y^4-x^4)
i really have a hard time in factoring long expressions. is there any technique? thanks

2. i really have a hard time in factoring long expressions. is there any technique?
Yes ...PRACTISE (I hope the spelling is right)

3. i didn't get the answer..

is this correct??

4. Originally Posted by princess_21
is this correct??
Please reply showing the steps you used to arrive at the above, so that we can try to help you find the error(s).

Thank you!

5. Originally Posted by princess_21

is this correct??

x^4 y^2 - y^2 z^4 - x^2 y^4 + x^2 z^4 + y^4 z^2 - x^4 z^2

x^2y^2 (x^2-y^2) + z^4 (x^2-y^2) - z^2 (x^4-y^4)
(x^2 -y^2) (x^2y^2 -z^4 - x^2z^2 - y^2z^2)
(x^2 -y^2) x^2(y^2-z^2) - z^2 (y^2-z^2)
(x^2 -y^2) (x^2-z^2) (y^2-z^2)

(x-y)(x+y)(x-z)(x+z)(y-z)(y+z)

6. Its correct beyond any doubt and I must say You did well

7. You started with $y^2(x^4\, -\, z^4)\, -\, x^2(y^4\, -\, z^4)\, +\, z^2(y^4\, -\, x^4)$

Originally Posted by princess_21
x^4 y^2 - y^2 z^4 - x^2 y^4 + x^2 z^4 + y^4 z^2 - x^4 z^2
In the above, you multiplied everything out to get:

. . . . . $x^4 y^2\, -\, y^2 z^4\, -\, x^2 y^4\, +\, x^2 z^4\, +\, y^4 z^2\, -\, x^4 z^2$

There appear to be some steps missing between the above and your next step:

Originally Posted by princess_21
x^2y^2 (x^2-y^2) + z^4 (x^2-y^2) - z^2 (x^4-y^4)
I think you regrouped and then factored out of pairs of terms, as:

. . . . . $x^4 y^2\, -\, x^2 y^4\, +\, x^2 z^4\, -\, y^2 z^4\, -\, x^4 z^2\, +\, y^4 z^2$

. . . . . $x^2 y^2 (x^2\, -\, y^2)\, +\, z^4 (x^2\, -\, y^2)\, -\, z^2 (x^4\, -\, y^4)$

Then you factored the difference of squares in the last set of parentheses above, and factored " $x^2\, -\, y^2$" out front:

. . . . . $x^2 y^2 (x^2\, -\, y^2)\, +\, z^4 (x^2\, -\, y^2)\, -\, z^2 \left[(x^2\, -\, y^2)(x^2\, +\, y^2)\right]$

. . . . . $(x^2\, -\, y^2)\left[x^2 y^2\, +\, z^4\, -\, z^2(x^2\, +\, y^2)\right]$

. . . . . $(x^2\, -\, y^2)(x^2 y^2\, +\, z^4\, -\, x^2 z^2\, -\, y^2 z^2)$

You then paired and factored inside the second parentheses:

. . . . . $(x^2\, -\, y^2)(x^2 y^2\, -\, x^2 z^2\, -\, y^2 z^2\, +\, z^4)$

. . . . . $(x^2\, -\, y^2)\left[x^2(y^2\, -\, z^2)\, -\, z^2(y^2\, -\, z^2)\right]$

. . . . . $(x^2\, -\, y^2)\left[(y^2\, -\, z^2)(x^2\, -\, z^2)\right]$

Then you factored the differences of squares:

. . . . . $(x\, -\, y)(x\, +\, y)\left[(y\, -\, z)(y\, +\, z)(x\, -\, z)(x\, +\, z)\right]$

This wasn't the factored form I'd expected, but it looks to be correct. Good job!

8. thanks, then what did you expect?

9. Originally Posted by princess_21
what did you expect?
I'd expected a sum of squares, at some point. But the "plus" and "minus" signs worked out such that this was avoided.