Question

Step-by-step solution on how to factor (x-y-2z)^2-(2x+y-z)^2

Answer 1

use the identiy : \(a^2-b^2 = (a+b)(a-b)\)

Answer 2

@ganeshie8 yes, but would you mind showing the full solution?

Answer 3

give it a try, i can have a look once u r done :)

Answer 4

@ganeshie8 tried it already, but i seem to be getting the signs all mixed up. here's what i keep getting:\[=(x-y-2z+2x+y-z)(x-y-2z-2x-y+z)\]\[=(3x-3z)(-x-2y-z)\]\[=3(x-z)(-x-2y-z)\] but the correct answer is actually 3(z-x)(x+2y+z)

Answer 5

Excellent ! your answer is also correct

Answer 6

=3(x-z)(-x-2y-z)
=-3(x-z)(x+2y+z)

Answer 7

=3(x-z)(-x-2y-z)
=-3(x-z)(x+2y+z)
= 3(z-x)(x+2y+z)

Answer 8

@ganeshie8 but i was not able to come up with a negative answer... i checked my answer again and i did not bring out a negative sign even if my answer is just the negative of the correct answer.

Answer 9

u got the below answer :-
3(x-z)(-x-2y-z)

right ?

Answer 10

take -1 common in last factor and see wat u get

Answer 11

@ganeshie8 yes, but i don't understand where the -1 is coming from...?

Answer 12

3(x-z)(-x-2y-z)
^ ^ ^

Answer 13

(-a-b-c)

can be written as

-(a+b+c)

Answer 14

this much should be easy to see ha ?

Answer 15

@ganeshie8 i got the answer 3(x-z)(-x-2y-z) whereas the correct is 3(z-x)(x+2y+z) but wouldn't my answer only be correct if there were a negative sign before it? because my answer is the negative of the correct answer but clearly, there is no negative sign before my answer, making both answers positive; thus, totally different. am i missing something?

Answer 16

yes u r overlooking another thing

Answer 17

in ur answer, u have (x-z)

Answer 18

where as the so called correct answer, u have (z-x)

Answer 19

getting ? :)

Answer 20

so both are same

Answer 21

(x-z) = -(z-x)

Answer 22

@ganeshie8 i understand clearly that (x-z)=-(z-x) but the thing is both answers are POSITIVE as in, (x-z) and (z-x), there is NO NEGATIVE SIGN... so....? is my question confusing you?

Answer 23

whats ur question ?

Answer 24

@ganeshie8 that my answer (x-z) is DIFFERENT from the correct one which is (z-x). so how do i get to the correct answer (z-x) from my answer (x-z) if my answer is not the negative of the correct answer? would you mind showing your solution to make everything clearer? i i find it a bit hard to understand without showing the actual figures.

Answer 25

i gave u the solution already above, maybe, just lay back and look at it again you will see. good luck !

Answer 26

my 4th reply has the solution

Answer 27

\begin{align}
\large 3(x-z)(-x-2y-z) &=\large 3(x-z)\cdot \color{red}{-1}(x+2y+z) \\
&=\large \color{red}-3(x-z)(x+2y+z) \\
&=\large -3(x-z)(x+2y+z) \\
\end{align}

Answer 28

In reference to what @ganeshie8 was talking about.