Factorise :

$(i) 6 x^{3} - 8 x^{2} (i i) 35 a^{3} b^{2} c + 42 a b^{2} c^{2} (i i i) 36 x^{2} y^{2} - 30 x^{3} y^{3} + 48 x^{3} y^{2} (i v) 8 (2 a + 3 b)^{3} - 12 (2 a + 3 b)^{2} (v) 9 a (x - 2 y)^{4} - 12 a (x - 2 y)^{3}$

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Solution

$(i) 6 x^{3} - 8 x^{2} = 2 x^{2} (3 x - 4) (i i) 35 a^{3} b^{2} c + 42 a b^{2} c^{2} = 7 a b^{2} c (5 a^{2} + 6 c) (i i i) 36 x^{2} y^{2} - 30 x^{3} y^{3} + 48 x^{3} y^{3} = 6 x^{2} y^{2} (6 - 5 x y + 8 x y) (i v) 8 (2 a + 3 b)^{3} - 12 (2 a + 3 b)^{2} = 4 (2 a + 3 b)^{2} [2 (2 a + 3 b) - 3] = 4 (2 a + 3 b)^{2} [4 a + 6 b - 3] (v) 9 a (x - 2 y)^{4} - 12 a (x - 2 y)^{3} = 3 a (x - 2 y)^{3} 3 (x - 2 y) - 4 = 3 a (x - 2 y)^{3} (3 x - 6 y - 4)$

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