If a + b = 56 and (a - b)2 = 496, find the value of the product of a and b.

Explanation

Given: a + b = 56 and (a - b)2 = 496 Formula used: (a + b)2 = a2 + b2 + 2ab (a - b)2 = a2 + b2 - 2ab Calculation: (a - b)2 = a2 + b2 - 2ab ⇒ (a - b)2 = ((a + b)2 - 2ab) - 2ab ⇒ (a - b)2 = (a + b)2 - 4ab Putting the given values of (a - b)2 = 496 and a + b = 56 into the above equation, we get: 496 = 562 - 4ab ⇒ 4ab = 3136 - 496 ⇒ 4ab = 2640 ⇒ ab = 660 Answer: Hence, the value of the product of a and b is '660'.