What is x(y-z)-z(x-y)-y(x-z) ?

The solution to x(y-z)-z(x-y)-y(x-z) is 2yz-2xz

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simplify x(y-z)-z(x-y)-y(x-z)

simplify

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

2 yz - 2 x z

Solution steps

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

Expand

x (y - z) : x y - x z

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

Expand

- z (x - y) : - x z + yz

= x y - x z - x z + yz - y (x - z)

Expand

- y (x - z) : - x y + yz

= x y - x z - x z + yz - x y + yz

Add similar elements:

- x z - x z = - 2 x z

= x y - 2 x z + yz - x y + yz

Group like terms

= x y - x y + yz + yz - 2 x z

Add similar elements:

x y - x y = 0

= yz + yz - 2 x z

Add similar elements:

yz + yz = 2 yz

= 2 yz - 2 x z

12 + 13 m + m^{2}

w^{2} - 25

2 x^{2} + 5 x - 3 = 9

0 = 12 x^{2} - 24 x

4 x^{2} - 8 = 56