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ALGEBRA ALGEBRA be = (x2 - y2)2-C2 2 b a - 4-691- b -C2 = (Putting the value of x, y) 12 b - = 13. Factorise : 3-7x + 4x2 Sol. 3 - 7x + 4x2 = 3-3x - 4x + 4x2 = 3 (1 - x) - 4x (1 – x) = (1-x) (3 - 4x) 14. Factorise : 9x4 + 4y4 - 13xyukle Sol. 9x4 + 4y4 - 13x+y? =9x4 - 13x+y + 4y4 - 9x4-9xy - 4x+y + 4y = 9x? (x2 - y2) – 4y(x? - y^) (x - y) (9x2 - 4y?) = x - y) (x + y) (3x - 2y) (3x + 2y) 15. Factorise : (2a + 3b)2 – 14 (2a + 3b) (3a-b) - 32 (3a - b)2 Sol. Let (2a + 3b) = x and (3a-b) = y .. Expression = xé – 14xy-32y2 = x - 16xy + 2xy - 32y2 = x (x-16y) + 2y (x - 16y) (x - 16y) (x + 2y) [(2a + 3b) – 16 (3a - b)] (2a + 3b) + 2 (3a-b)] (19b-46a) (8a + b) 16. Factorise : (2x - 3y)2 - 10x+ 154-6) Sol. (2x - 3y)2 - 5 (2x-3y) - 6 Let (2x - 3y) = a = a2-5a-6 = a - 6a+ a-6 = a (a - 6) + 1 (a-6) = (a-6) (a + 1) - 2 a b2 ba? b2 + + 2 Х + 2 b2a? a 62 a² = (4)2 - 2 = (4 + c) (4 - C) 19. Factorise : 27x3-125y3 Sol. 27x3 - 125y3 = (3x)3 – (5y) = (3x - 5y) [(3x)2 + 3x x 5y + (5y)?: Joa = (3x - 5y) (9x2 + 15xy + 25y) 20. Factorise : 64 - X6 Sol. 64 - X (8)2 – (x3) - (8 + x)(8 - x) (23 + x°) (23 – x3) - (2 + x) [(2)2 - 2 x x + xº] (2 - x) (22 + 2 x x + x?) = (2 + x) (4 - 2x + x) (2-x) (4 + 2x + xº) 21. Factorise : (x + y)2 + (x - y)3 Sol. Let (x + y) = a, (x - y) = b :: Expression = a + b3 ELLO = (a + b) (a2 - ab + b) = (x + 4 + x-u) [(x + ul2 - (x + u) (x-u) + (x-u)21 = = ...
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