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Which of the following is obtained by subtracting x2−y2 from y2−x2?
−2(x2−y2)
−2(x2+y2)
2(x2+y2)
2(x2−y2)
−2(x2−y2)
Distribute the negative sign carefully across both terms to combine like powers of x and y.
Expression to subtract: x2−y2, Expression from which to subtract: y2−x2
(y2−x2)−(x2−y2)
Distribute the negative sign carefully across both terms to combine like powers of x and y.
Subtracting the wrong way around or forgetting to distribute the negative sign to −y2, leading to an incorrect sign.
Set up the subtraction expression
To subtract (x2−y2) from (y2−x2), write it in the form: (y2−x2)−(x2−y2)
(y2−x2)−(x2−y2)
Remove the parentheses and distribute the negative sign
Distribute the negative sign to each term inside the second parenthesis: y2−x2−x2+y2
y2−x2−x2+y2
Combine like terms
Group the y2 terms and the x2 terms together: (y2+y2)+(−x2−x2)=2y2−2x2
2y2−2x2
Factor out −2
Factor out −2 to match the standard options format: −2(x2−y2)
−2(x2−y2)
A is correct because subtracting x2−y2 from y2−x2 yields −2(x2−y2).
Always verify subtraction order ('subtract A from B' means B - A) to avoid sign inversion errors in competitive exams.
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