If loga+ logb=logab show that (a+b)²-(a-b)²=4ab
(a+b)²-(a-b)²
a²+2ab+b² - (a²-2ab+b²)
= 4ab
not sure what the logs have to do with anything here.
To show that (a+b)² - (a-b)² = 4ab, we can first expand both sides of the equation.
Starting with the left side, (a+b)² - (a-b)², we can use the identity a² - b² = (a+b)(a-b). Applying this identity twice, we get:
(a+b)² - (a-b)² = [(a+b)+(a-b)][(a+b)-(a-b)]
Simplifying this expression, we have:
[(a+b)+(a-b)][(a+b)-(a-b)] = [2a][2b] = 4ab
Thus, we can conclude that (a+b)² - (a-b)² = 4ab.