2 38. ( ) ( ) 16 + 8x 2 + x 4 = (4 + x 2 ) 2 2 2 = 3x ( x + 3)(x − 3) 3x − 27 x = 3x (x − 9) = (2 − x) (2 + x ) 16 − 8 x 2 + x 4 = (4 − x 2 ) 5x + 30 x + 45x = 5x ( x + 6 x + 9) = 5x ( x + 3) 16 − x 4 = (4 + x 2 )(4 − x 2 ) = (4 + x 2 )(2 + x)(2 − x) 2 2 2 mcm 2 ⋅ 3⋅ 5x (x + 3) ( x − 3) ⇒ 30 x ( x + 3) (x − 3) mcm (4 + x 2 ) (2 + x) (2 − x) 34. 3 − 3a = 3(1 − a ) = 3 (1 + a )(1 − a ) 39. 1 + a = 1 + a 6 + 6a = 2 ⋅ 3 (1 + a ) (1 + a ) = (1 + a) 12 + 12a = 2 ⋅ 3 (1 + a ) 1 + a = (1 + a )(1 − a + a ) 9 − 9a = 3 (1 − a ) mcm (1 + a ) (1 − a + a )(1 + a ) mcm 2 ⋅ 3 (1 + a )(1 + a )(1 − a ) 40. 8n − 10n − 3 = (8n) − 10 (8n) − 24 ⇒ 36 (1 + a )(1 − a ) = 36 (1 − a ) = [(8n − 12)(8n + 2)] ÷ 4 ⋅ 2 = (2n − 3)(4n + 1) 2 (3n − 2) = 2 (3n − 2) 35. 20n + 13n + 2 = ( 20n) + 13 ( 20n) + 40 135n − 40 = 5 (27n − 8) = 5 (3n − 2)(9n + 6n + 4) = [(20n + 8)(20n + 5)] ÷ 4 ⋅ 5 = (5n + 2)(4n + 1) 12n − 8 = 2 (3n − 2) 10n − 11n − 6 = (10n) − 11(10n) − 60 = [(10n − 15)(10n + 4)] ÷ 5⋅ 2 = (2n − 3)(5n + 2) mcm 5⋅ 2 (3n − 2) (9n + 6n + 4) mcm (2n − 3)(5n + 2)(4n + 1) ⇒ 20(3n − 2) (9n + 6n + 4) 41. 6a + ab − 2b = 36a + 6ab − 12b 36. 12mn + 8m − 3n − 2 = 4m (3n + 2) − (3n + 2) = [(6a + 4b)(6a − 3b)] ÷ 2 ⋅ 3 = (4m − 1)(3n + 2) = (3a + 2b)(2a − b) 48m n − 3n + 32m − 2 = 16m (3n + 2) − (3n + 2) (15a) + 22b (15a ) + 120b + + = 15 a 22 ab 8 b = (16m − 1)(3n + 2) = [(15a + 12b)(15a + 10b)] ÷ 3⋅ 5 = (4m + 1)(4m − 1)(3n + 2) = (5a + 4b)(3a + 2b) 6n − 5n − 6 = (6n) − 5( 6n) − 36 10a + 3ab − 4b = (10a) + 3b (10a) − 40b = [(6n − 9)(6n + 4)] ÷ 3⋅ 2 = [(10a + 8b)(10a − 5b)] ÷ 2 ⋅ 5 = (2n − 3)(3n + 2) = (5a + 4b)(2a − b) mcm (4m + 1)(4m − 1)(3n + 2)(2n − 3) mcm (3a + 2b) (2a − b)(5a + 4b) ⇒ (16m − 1) (3n + 2)(2n − 3)
33. 2 x 3 − 12 x 2 + 18 x = 2 x x 2 − 6 x + 9 = 2 x x − 3 4
3
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2 3 2 3 2 37. 15a x + 16a x − 15a x = a x (15x + 16 x − 15) 2
5
2
[
]
2 = a 2 x 3 (15x ) + 16 (15x ) − 225
=a x 2
3
18 x + 60x + 50 x = 2 x (9 x + 30 x + 25) 2
[
= (3x + 2 y )(4 x − y )
15x + 13xy + 2 y = (15x ) + 13 y (15x ) + 30 y 2 2
]
2 = 2 x ( 9 x ) + 30 ( 9 x ) + 225
[
[
]
= (3x + 2 y )(5x + y )
20 x 2 − xy − y 2 = (20 x ) − y (20 x ) − 20 y 2 2
[
12ax 3 + 20ax 2 = 2 2 ax 2 (3x + 5)
= (4 x − y )(5x + y )
2
= 4a 2 x 3 (3x + 5) (5x − 3) 2
]
= (20 x − 5 y )(20 x + 4 y ) ÷ 5⋅ 4
2
mcm = 22 a 2 x 3 (3x + 5) (5x − 3)
]
= (15x + 10 y )(15x + 3 y ) ÷ 5⋅ 3
= 2 x (9 x + 15)(9 x + 15) ÷ 3⋅ 3 = 2 x (3x + 5)
2
2
2
[
]
= (12 x + 8 y )(12 x − 3 y ) ÷ 4 ⋅ 3
[(15x + 25)(15x − 9) ÷ 5⋅ 3]
= a 2 x 3 (3x + 5)(5x − 3)
3
2 2 2 42. 12 x + 5xy − 2 y = (12 x ) + 5 y (12 x ) − 24 y 2
4
mcm
(4 x − y)(5x + y)(3x + 2 y)