Question 142

Four of the following five parts numbered A,B,C,D,E are in the following equation are exactly equal.Which of the part is not equal to the other four.The number of that part is the answer

Solution

(A) : $$xy^{2}-x^{2}y+2x^{2}y^{2}$$

= $$xy(y-x+2xy)$$

(B) : $$xy^{2}(1-2x)+x^{2}y(2y-1)$$

= $$(xy^2-2x^2y^2)+(2x^2y^2-x^2y)$$

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

(C) : $$xy^{2}(1-2x)+x^{2}y(2y-1)$$

= $$(xy^2-2x^2y^2)+(2x^2y^2-x^2y)$$

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

(D) : $$xy[y(1+x)-x(1+y)]$$

= $$xy(y+xy-x-xy) = xy(y-x)$$

(E) : $$xy[(x+y)^{2}+y(1-y)-x(1+x)-2xy]$$

= $$xy[(x^2+y^2+2xy)+(y-y^2)+(-x-x^2)-2xy]$$

= $$xy(y-x)$$

=> Ans - (A)

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