Question

Simplificando a expressão (a + 2b)² - (a+b)(a - b):

Answer 1

(a + 2b)² - (a+b)(a - b)
a² +2.(a).(2b) + (2b)² - (a² -ab +ab -b²)
a² + 4ab + 4b² -a² +ab -ab +b²
a² -a² +4ab+ab -ab +4b² +b²    elimina a² -a²
5ab -ab +5b²
4ab +5b²
b(4a +5b)

Answer 2

$(a + 2b)^2 - (a+b)(a - b)\\a^2 +2.a.2b + (2b)^2 - (a^2 -ab +ab -b^2)\\a^2 + 4ab + 4b^2 -a^2 +ab -ab +b^2\\a^2 -a^2 +4ab+ab -ab +4b^2 +b^2\\5ab -ab +5b^2\\\boxed{5b^2 + 4ab}$