Testing Math Tag
\( ((\frac{1}{2})(x+y))^2-((\frac{1}{2})(x-y))^2 \)
The mean of x and y, squared, minus the the distance from the mean of x and y, squared.
= \( [\frac{1}{4} (x+y)^2] - [\frac {1}{4} (x-y)^2] \)
By squaring \( \frac{1}{2} \) on both occasions.
= \( [\frac{x^2+2xy+y^2}{4}] - [\frac{x^2-2xy+y^2}{4}] \)
By distribution.
= \( \frac{x^2}{4} + \frac{xy}{2} + \frac{y^2}{4} - \frac{x^2}{4} + \frac{xy}{2} - \frac{y^2}{4} \)
By separating terms.
= \( \frac{2xy}{2} \)
By cancelling, by simplifying like terms.
= \( xy \)
By simplifying, by dividing by \( \frac{2}{2} \)
Thus proves that for any two given numbers x and y,
xy equals the square of the mean of x and y, minus the square of the distance from the mean of x and y.