Factorize the following expression : \(a^2 + b^2 + 2(ab + bc + ca)\)

\[ a^2 + b^2 + 2(ab + bc + ca) \] \[ = a^2 + b^2 + 2ab + 2bc + 2ca \] \[ = (a + b)^2 + 2c(a + b) \] \[ = (a + b)^2 + 2c(a + b) + c^2 – c^2 \] \[ = (a + b + c)^2 – c^2 \] \[ = (a + b + c – c)(a + b + c + c) \] \[ = (a + b)(a + b + 2c) \]