Question

Simplify the following expression: $x\left( y-z \right)-y\left( z-x \right)-z\left( x-y \right)$
A. $2x\left( y-z \right)$
B. $2y\left( z-x \right)$
C. $2x\left( z-y \right)$
D. None of the above

Answer 1

Hint: Here we have been given an expression and we have to simplify it. As the terms in the expressions are all variables we will simply open the brackets and multiply them with the outside values. Then we will take the common terms together and simplify them to get a value. Finally we will take the common term outside from the values obtained and get our desired answer.

Complete step by step answer:
The expression is given as follows,
$x\left( y-z \right)-y\left( z-x \right)-z\left( x-y \right)$
Now we will multiply the terms outside the bracket with the term inside the bracket as follows,
$\Rightarrow x\times y+x\times -z-y \times z-y \times -x-z \times x-z \times -y$
$\Rightarrow xy-xz-yz+xy-xz+yz$
Taking the common terms together we get,
$\Rightarrow \left( xy+xy \right)+\left( -xz-xz \right)+\left( -yz+yz \right)$
$\Rightarrow 2xy-2xz$
Taking $2x$ common we get,
$\Rightarrow 2x\left( y-z \right)$
So we get the answer as $2x\left( y-z \right)$
Hence the correct option is option (A).

Note:
For simplifying the expression we should know how to combine like terms, how to factor a number and the order of the operations. We start by simplifying the brackets first then according to the BODMAS (Brackets, Of, Divide, Multiply, Addition and Subtraction) rule we do the operation on the terms given and get our answer. For getting a more compact answer we have taken common terms outside. When we multiply positive or negative numbers or variables it can cause confusion which is to be taken care of. Always remember two “pluses” makes a plus, two “minuses” makes a plus and a “plus” and a “minus” makes a minus. Algebraic expressions are the expression made up of variables and constants along with the algebraic operations; it is different from an algebraic equation as it doesn't have an equal sign.