8.Factorize each of the following :
i)$$8a^3 + b^3 + 12a^2b + 6ab^2$$
ii)$$8a^3 - b^3 - 12a^2b + 6ab^2$$
iii)$$27 - 125a^3 - 135a + 225a^2$$
iv)$$64a^3 - 27b^3 - 144a^2b + 108ab^2$$
v)$$27p^3 - 1/216 - 9p^2/2 + p/4$$

i)$$8a^3 + b^3 + 12a^2b + 6ab^2$$
i.e.,$$= (2a)^3 + b^3 +3(2a)(b)(2a + b))$$
by using identity $$(a + b)^3 = a^3 + b^3 + 3ab(a + b)$$
$$= (2a)^3 + b^3$$

ii)$$8a^3 - b^3 - 12a^2b + 6ab^2$$
i.e.,$$= (2a)^3 - b^3 -3(2a)(b)(2a - b)$$
by using identity $$(a - b)^3 = a^3 - b^3 - 3ab(a - b)$$
$$= (2a)^3 - b^3$$

iii)$$27 - 125a^3 - 135a + 225a^2$$
i.e.,$$= (3)^3 - (5a)^3 -3(3)(5a)(3 - 5a)$$
by using identity $$(a - b)^3 = a^3 - b^3 - 3ab(a - b)$$
$$= (3)^3 - 5a^3$$

iv)$$64a^3 - 27b^3 - 144a^2b + 108ab^2$$
i.e.,$$= (4a)^3 - (3b)^3 -3(4a)(4b)(4a - 3b))$$
by using identity $$(a - b)^3 = a^3 - b^3 - 3ab(a - b)$$
$$= (4a)^3 - (3b)^3$$

v)$$(27p^3 - 1/216 - 9p^2/2 + p/4$$
i.e.,$$= (3p)^3 - (1/6)^3 -3(3p)(1/6)(3p - 1/6))$$
by using identity $$(a - b)^3 = a^3 - b^3 - 3ab(a - b)$$
$$= (3p)^3 - {1/6}^3$$