Question

A expressão (a+b)² + (a-b) . (a+b) - (a-b)²é igual a...

Answer 1

(a+b)² + (a-b) . (a+b) - (a-b)²

(a+b).(a+b) + (a+b) . (a-b) - (a-b).(a-b)

a²+ab+ab+b²+a²+ab-ab+b²- a²-ab-ab+b²

a²+2ab+b²+a²+b²-a²-2ab+b²

a²+3b²

Answer 2

$(a+b)^2=a^2+2ab+b^2$
$(a-b)^2=a^2-2ab+b^2$
$(a+b)(a-b)=a^2-b^2$

$(a+b)^2 + (a-b) . (a+b) - (a-b)^2=\\(a^2+2ab+b^2)+(a^2-b^2)-(a^2-2ab+b^2)=\\a^2+2ab+b^2+a^2-b^2-a^2+2ab-b^2=\\a^2+a^2-a^2+2ab+2ab+b^2-b^2-b^2=\\a^2+4ab-b^2$