Question & Answer

The value of the product of (x-y) and (y-x) is


ANSWER Verified Verified
Hint: To solve the given question which is calculating the product of (x-y) and (y-x) we proceed using the necessary algebraic calculations and properties of the product of (x-y) with (y-x). To do so we first open one of the brackets, preferably the first one, and then taking the second one as a product of elements of the first bracket. Proceeding in this way we obtain the required result.

Complete step-by-step answer:
We have to calculate the value of the product of (x-y) and (y-x).
Multiplying (x-y) with (y-x) we have,

Expanding the above by opening from the left and taking x and y simultaneously common we have,

Again, opening the right-hand side of the equation, taking x and y inside and multiplying respectively with (y-x) we get,

Now substituting xx as x2 and yy as y2 we have,
Replacing xy by yx in the above equation we have,

Making necessary rearrangements in the above obtained equation we have,

Adding xy to xy and making it equal to 2xy we have,

Hence, we obtain \[(x-y)(y-x)=2xy-{{x}^{2}}-{{y}^{2}}\], which is the required solution of the question.

Matching from the options given in the question we have option (c) as the correct option.

Note: The possibility of error in the question is taking wrong signs in common while multiplying x and y with (y-x) or (x-y). If we take calculation errors in the signs of x and y then it will lead to cancellation of certain terms in the expression and will ultimately give wrong solutions as a result.