Factorise :

$\dfrac{1}{35} + \dfrac{12}{35}a + a^2$

Given,

$\phantom{=}\dfrac{1}{35} + \dfrac{12}{35}a + a^2 \\[1em] = a^2 + \dfrac{12}{35}a + \dfrac{1}{35} \\[1em] = \dfrac{35a^2 + 12a + 1}{35} \\[1em] = \dfrac{35a^2 + 5a + 7a + 1}{35} \\[1em] = \dfrac{5a(7a + 1) + 1(7a + 1)}{35} \\[1em] = \dfrac{(7a + 1)(5a + 1)}{35}.$

Hence, $\dfrac{1}{35} + \dfrac{12}{35}a + a^2 = \dfrac{(7a + 1)(5a + 1)}{35}$.