Factor k^2+(2k+1)

$k^{2} + (2 k + 1)$

Remove parentheses.

$k^{2} + 2 k + 1$

Factor using the perfect square rule.

Rewrite $1$ as $1^{2}$ .

$k^{2} + 2 k + 1^{2}$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$2 k = 2 \cdot k \cdot 1$

Rewrite the polynomial.

$k^{2} + 2 \cdot k \cdot 1 + 1^{2}$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = k$ and $b = 1$ .

${(k + 1)}^{2}$