3 Tutor System
Starting just at 265/hour

# 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)$$27p^3 - \frac{1}{216} - \frac{9p^2}{2} + \frac{p}{4}$$

i)$$8a^3 + b^3 + 12a^2b + 6ab^2$$
$$= (2a)^3 + b^3 +3(2a)(b)(2a + b))$$
$$[\because (a + b)^3 = a^3 + b^3 + 3ab(a + b)]$$
$$= (2a)^3 + b^3$$

ii)$$8a^3 - b^3 - 12a^2b + 6ab^2$$
$$= (2a)^3 - b^3 -3(2a)(b)(2a - b)$$
$$[\because (a - b)^3 = a^3 - b^3 - 3ab(a - b)]$$
$$= (2a)^3 - b^3$$

iii)$$27 - 125a^3 - 135a + 225a^2$$
$$= (3)^3 - (5a)^3 -3(3)(5a)(3 - 5a)$$
$$[\because (a - b)^3 = a^3 - b^3 - 3ab(a - b)]$$
$$= (3)^3 - 5a^3$$

iv)$$64a^3 - 27b^3 - 144a^2b + 108ab^2$$
$$= (4a)^3 - (3b)^3 -3(4a)(4b)(4a - 3b))$$
$$[\because (a - b)^3 = a^3 - b^3 - 3ab(a - b)]$$
$$= (4a)^3 - (3b)^3$$

v)$$(27p^3 - \frac{1}{216} - \frac{9p^2}{2} + \frac{p}{4}$$
$$= (3p)^3 - (\frac{1}{6} )^3 -3(3p)(\frac{1}{6})(3p - 1/6))$$
$$[\because (a - b)^3 = a^3 - b^3 - 3ab(a - b)]$$
$$= (3p)^3 - (\frac{1}{6})^3$$