Question

Simplify : x(y-z)-y(z-x)-z(x-y)​

Answer 1

Step-by-step explanation:

xy-xz-yz+yx-zx+zy

xy+yx-xz-zx-yz+yz

2xy-2xz

In this I have first multiplied the outer variable with inside variable and then wrote same terms (zx may be writen as xz and others too)And then calculated them.

Your answer will be 2xy-2xz because +yz has cancelled -yz.

If liked my answer please follow.

Answer 2

Answer:

2$xy$ - 2$xz$

Step-by-step explanation:

$x$ ( $y$ - $z$ ) - $y$( $z$ - $x$ ) - $z$( $x$ - $y$ ) =

It's easy to solve this if you solve it as though they are numbers :

Firstly, solve the brackets.

Remember :

Negative Multiplied by Negative is Positive ;

Positive Multiplied by Negative is Negative :

Positive Multiplied by Positive is Positive.

So,

$x$ ( $y$ - $z$ ) - $y$( $z$ - $x$ ) - $z$( $x$ - $y$ ) = $xy$ - $xz$ - $yz$ + $xy$ - $zx$ + $zy$

To make it clearer :

( $x$ × $y$ ) + ( $x$ × $- z$ ) + ( $-y$ × $z$ ) + ( $-y$ × $-x$ ) + ( $-z$ × $x$ ) + ( $-z$ × $-y$ )

= ( $xy$ ) + ( - $xz$  ) + ( - $yz$ ) + ( + $xy$ ) + ( - $zx$ ) + ( + $zy$ )

= $xy$ - $xz$ - $yz$ + $xy$ - $zx$ + $zy$

Now group it together.

Note : - $xz$ and - $zx$ is the same.

( $x$ × $y$ ) + ( $x$ × $- z$ ) + ( $-y$ × $z$ ) + ( $-y$ × $-x$ ) + ( $-z$ × $x$ ) + ( $-z$ × $-y$ )

= ( $xy$ ) + ( - $xz$  ) + ( - $yz$ ) + ( + $xy$ ) + ( - $zx$ ) + ( + $zy$ )

= $xy$ - $xz$ - $yz$ + $xy$ - $zx$ + $zy$

=  $xy$ + $xy$ - $xz$ - $xz$ - $yz$ + $yz$

Now solve it.

( $x$ × $y$ ) + ( $x$ × $- z$ ) + ( $-y$ × $z$ ) + ( $-y$ × $-x$ ) + ( $-z$ × $x$ ) + ( $-z$ × $-y$ )

= ( $xy$ ) + ( - $xz$  ) + ( - $yz$ ) + ( + $xy$ ) + ( - $zx$ ) + ( + $zy$ )

= $xy$ - $xz$ - $yz$ + $xy$ - $zx$ + $zy$

=  $xy$ + $xy$ - $xz$ - $xz$ - $yz$ + $yz$

= 2$xy$ - 2$xz$

2$xy$ - 2$xz$  is your answer.