Question

Add and simplify of x(x-y),y(y-z),z(z-x)

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Answer 1

Concept:

Solving a math problem involves simplifying an expression. When you simplify an expression, you're essentially attempting to write it in the most straightforward manner feasible. No more addition, subtracting, multiplying, or dividing should be done at the conclusion.

Given:

The expressions to add and simplify are $x(x-y), y(y-z), z(z-x).$

Find:

Add and simplify  $x(x-y), y(y-z), z(z-x).$

Solution:

Add the expressions

$x(x-y)+ y(y-z)+z(z-x)$        .......eq(1)

Simplify $x(x-y)$

$x(x-y)=x^{2} -xy$

Simplify $y(y-z)$

$y(y-z)=y^{2} -yz$

Similarly, simplify $z(z-x)$

$z(z-x)=z^{2} -zx$

Put values of simplified expressions in eq(1)

$x^{2} -xy+y^{2}-yz+ z^{2}-zx$

Or

$x^{2}+y^{2}+ z^{2} -xy-yz-zx$

This can't be simplified further.

Hence after adding and simplifying the final expression is $x^{2}+y^{2}+ z^{2} -xy-yz-zx.$

Answer 2

Algebraic expressions are the equations we get when operations such as addition, subtraction, multiplication, division, etc. are operated upon by any variable.

The given expression is $x(x-y),y(y-z),z(z-x)$ add and simplify the given expression.

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

$x^2-xy+y^2-yz+z^2-zx$

So, the simplify value is

$x^2+y^2+z^2-xy-yz-zx$