When the square of the difference of two natural numbers is subtracted from the square of the sum of the same two numbers and the result is divided by four, we get
Explanation:
Let the two numbers be hx and hy, where h is the HCF of thest two numbers and LCM of these numbers = hxy.
Now, (hx + hy)2 - (hx - hy)2 = (hx)2 + (hy)2 + 2h2xy - ((hx)2 + (hy)2 - 2h2xy) = 4h2xy = 4 × h × hxy = 4 × HCF × LCM
Hence, option (a).
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