Question

Fatore:

(a + 1)² + 2 (a + 1) + 1

Answer 1

$(a + 1)^{2} + 2 .(a + 1) + 1$

$(a + 1).[(a + 1)+2]+1$

$(a + 1).[a + 3]+1$

$(a + 1).(a + 3)+1$

$a^{2} +3a+a+3+1$

$a^{2} +4a+4$

$(a+2)^{2}$

Answer 2

$(a + 1)^2 + 2 (a + 1) + 1 \\ \\ a^2 + a + a +1 + 2a + 2 + 1 \\ \\ a^2 + 2a + 1 + 2a + 3 \\ \\ => a^2 + 4a + 4$

Expressão fatorada:

$a^2 + 4a + 4 => (a + 2)^2$