NÅGRA KOMMENTARARER TILL LÖSNINGARNA
NÅGRA KOMMENTARARER TILL LÖSNINGARNA NÅGRA KOMMENTARARER TILL LÖSNINGARNA
4304d 2 2 4 x(3x − 1)(3 + x ) 2 4 2 4 x(9x + 3x −3 −x ) 36x + 12x −12x−4x x + x − x 3 5 3 5 3 12 32 12 4304g 5 x(3x− 2)(2x+ 3) 2 5 x(6x + 9x−4x−6) 3 2 2 30x + 45x −20x −30x 3 2 30x + 25x −30x 4307a 2 ( a + 5) a + 2⋅a⋅ 5+ 5 2 a + 10a+ 25 2 2 4307d 2 (3x+ 4 y) (3 x) + 2⋅3x⋅ 4 y+ (4 y) 2 2 9x + 24xy+ 16y 2 2 4308a ( x+ 5) + ( x−5) 2 2 2 2 2 2 ( x + 2⋅x⋅ 5+ 5 ) + ( x −2⋅x⋅ 5+ 5 ) 2 2 ( x + 10x+ 25) + ( x − 10x+ 25) 2 2 x + 10x + 25 + x −10x + 25 2 2x+ 50 LÖSNINGAR DEL B 4304e 0,5(10x + 3)(3−10 x) 0,5(3 + 10 x)(3−10 x) 2 2 0,5(3 + (10 x) ) 2 0,5(9 + 100 x ) 2 4,5 − 50x 4304h ⎛ a ⎞⎛ a ⎞ 10⎜1− ⎟⎜1+ ⎟ ⎝ 10 ⎠⎝ 10 ⎠ ⎛ a ⎞⎛ a ⎞ 10⎜1+ ⎟⎜1− ⎟ ⎝ 10 ⎠⎝ 10 ⎠ 2 ⎛ 2 ⎛ a ⎞ ⎞ 10 1 ⎜ ⎝ − ⎜ ⎟ ⎝10 ⎠ ⎟ ⎠ 2 ⎛ a ⎞ 10⎜1−⎟ ⎝ 100 ⎠ 4307b 2 ( x − 8) x −2⋅x⋅ 8+ 8 2 x − 16x+ 64 2 2 4307e 2 ( a+ 0,5 b) a + 2⋅a⋅ 0,5 b+ (0,5 b) 2 2 a + ab+ 0,25b 2 2 4308b ( ) 2 4304 f x y x y 40((5 x ) − ( y ) ) 4 4 40(25 x − y ) 4 4 1000x − 40y 40(5 2 + 2 )(5 2 − 2 ) 2 2 2 2 2 a 10⋅1−10⋅ 100 2 10 a 10⋅1− ⋅ 1 10 ⋅10 2 a 10 − 10 4307c 2 ( x+ 3 y) x + 2⋅x⋅ 3 y+ (3 y) 2 2 x + 6xy+ 9y 2 2 71 4307 f 2 2 2 (4x + 5 y ) (4 x ) + 2⋅4x ⋅ 5 y + (5 y ) 4 2 2 4 16x + 40x y + 25y 2 2 2 2 2 2 2 (2 a+ b) − 2a−b 2 2 2 2 ((2 a) + 2⋅2 a⋅ b+ b ) −((2 a) −2⋅2 a⋅ b+ b ) 2 2 2 2 (4a + 4 ab+ b ) −(4a − 4 ab+ b ) 4a 2 8ab 2 + 4ab + b 2 − 4a 2 + 4ab − b
2 LÖSNINGAR DEL B 4308c 2 2 ( x+ 4 y) −( x−4 y) −16xy 2 2 2 2 ( x + 2⋅x⋅ 4 y+ (4 y) ) −( x −2⋅x⋅ 4 y+ (4 y) ) −16xy 2 2 2 2 ( x + 8xy+ 16 y ) −( x − 8xy+ 16 y ) −16xy x 0 + 8xy 4309a 2 + 16y 2 2 2 − x + 8xy 2 − 16y − 16xy ⎛ x y⎞ ⎛ x ⎞ ⎜ + ⎟ − ⎜ + y⎟ ⎝3 4⎠ ⎝6 ⎠ 2 2 ⎛ x y⎞ ⎛ x y⎞ ⎜ + ⎟ − ⎜ + ⎟ ⎝3 4⎠ ⎝6 1⎠ 2 2 2 2 ⎛⎛ x⎞ 2 x y ⎛ y⎞ ⎞ ⎛⎛ x⎞ 2 x y ⎛ y⎞ ⎞ ⎜ + ⋅ ⋅ + − + ⋅ ⋅ + ⎜⎜ ⎟ ⎜ ⎟ ⎟ 3 1 3 4 4 ⎟ ⎜ ⎜⎜ ⎟ ⎜ ⎟ ⎟ 6 1 6 1 1 ⎟ ⎝⎝ ⎠ ⎝ ⎠ ⎠ ⎝⎝ ⎠ ⎝ ⎠ ⎠ 2 2 2 2 ⎛ x 2xy y ⎞ ⎛ x 2xy y ⎞ ⎜ + + ⎟− ⎜ + + ⎟ ⎝ 9 12 16⎠ ⎝36 6 1 ⎠ 2 2 2 2 x 2xy y x 2xy y + + − − − 9 12 16 36 6 1 ⎛1 1 ⎞ 2 ⎛ 2 2⎞ ⎛ 1 1⎞ 2 ⎜ − ⎟x + ⎜ − ⎟xy+ ⎜ − ⎟y ⎝9 36⎠ ⎝12 6 ⎠ ⎝16 1⎠ 2 2 1 2 1 15 2 x xy 15y x − xy− y = − − 12 6 16 12 6 16 4309b 2 2 4308d 2 ( x+ y)( x− y) −( x− y) x − y − x − xy+ y 2 2 2 2 ( ) ( 2 ) 2 x 2 2 − y − x + 2xy− y 2 − 2y + 2xy 2xy − 2y ⎛a b⎞ ⎜ + ⎟ ⎝3 4⎠ ⎛a b⎞⎛a b⎞ ⎛a b⎞ + ⎜ + ⎟⎜ − ⎟−⎜ − ⎟ ⎝3 4⎠⎝3 4⎠ ⎝3 4⎠ 2 2 2 2 2 2 ⎛⎛a⎞ 2 a b ⎛b⎞ ⎞ ⎛⎛a⎞ ⎛b⎞ ⎞ ⎛⎛a⎞ 2 a b ⎛b⎞ ⎞ ⎜ + ⋅ ⋅ + + − − − ⋅ ⋅ + ⎜⎜ ⎟ ⎜ ⎟ ⎟ ⎜⎜ ⎟ ⎜ ⎟ ⎟ ⎜⎜ ⎟ ⎜ ⎟ ⎟ ⎝3⎠ 1 3 4 ⎝4⎠ ⎟ ⎜⎝3⎠ ⎝4⎠ ⎟ ⎜⎝3⎠ 1 3 4 ⎝4⎠ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ 2 2 2 2 2 2 ⎛a 2ab b ⎞ ⎛a b ⎞ ⎛a 2ab b ⎞ ⎜ + + ⎟+ ⎜ − ⎟−⎜ − + ⎟ ⎝ 9 12 16⎠ ⎝ 9 16⎠ ⎝ 9 12 16 ⎠ 2 2 2 a 2ab b + + + 9 12 16 9 a 2 − 16 b 2 − 9 a 2 2ab b + − 12 16 2 2 a ab b + − 9 3 16 (Fel svar i vissa böcker) 2 2 72
- Page 21 and 22: 2102a 13 + −8 13 − 8 5 ( ) 2103
- Page 23 and 24: 2125a 3 310 ⋅ 30 = = 4 410 ⋅ 40
- Page 25 and 26: 2131a 2 ⎛ 1⎞ ⎛ 5 ⎛ 3 ⎞⎞
- Page 27 and 28: 2144b 3 3 4/2 − (4/2) 3 3 4/2−2
- Page 29 and 30: 2154a 3969 / -49 −81 ( ) 2155a 63
- Page 31 and 32: 2219a ( ) 2 3 10 49 + 4⋅ 125 −5
- Page 33 and 34: 2234a 1,890 2234b 0,845 LÖSNINGAR
- Page 35 and 36: 2349 Antag att grillen kostade A kr
- Page 37 and 38: 2415a x 2 = 2⋅2 x 2 = 2 ⋅2 x 2
- Page 39 and 40: 2433a 1 1 0,01 = = = 100 10⋅10 1
- Page 41 and 42: 2447a-b Antag att sidan är x m x
- Page 43 and 44: 2556a s = v⋅t (2547) meter 11 s
- Page 45 and 46: 2611a 2 x + + 4 y 2 3+ + 4 −2 3
- Page 47 and 48: 2640a A= 3b 3b= A 3b A = 3 3 A b =
- Page 49 and 50: 2671a 9 −( x − 3) = 20 9 −( x
- Page 51 and 52: 2705c 2r⋅ 4r = 8r 2 hela 2 ⋅
- Page 53 and 54: 2725a Antag att vattnet står x m h
- Page 55 and 56: 2748a 2400 12 pris per bok ⋅ 20 =
- Page 57 and 58: LÖSNINGAR DEL B 3129a Enligt randv
- Page 59 and 60: 3320d Likf ger 10 − x 9 = ( kors
- Page 61 and 62: LÖSNINGAR DEL B 3338 Antag att den
- Page 63 and 64: 3355 Antag att hypotenusan i stora
- Page 65 and 66: 4229a 2 ab( a −b) −a( ab −b)
- Page 67 and 68: 4239d 3 −( − 5m+ 8) = 36 −(1
- Page 69 and 70: 4245a A1+ A2 2 2 (2x + 20 x) + (2x
- Page 71: 4302a ( x+ 3)( x−3) 2 2 x − 3 2
- Page 75 and 76: 4329a Pytagoras sats ger ( x+ 18) =
- Page 77 and 78: LÖSNINGAR DEL B 4334 Antag att dom
- Page 79 and 80: 4410a 2 x − 3x+ 2= 0 3 x = ∓ 2
- Page 81 and 82: 4415 x x− = x+ + x(2x−1) − (
- Page 83 and 84: 4608 Antagande se figur 4609a 25 =
- Page 85 and 86: 4613 LÖSNINGAR DEL B a) Antag att
- Page 87 and 88: 4631a 4631b Antagande se figur LÖS
- Page 89 and 90: 5113a (3,7) (2,2) (8,4) d d a b
- Page 91 and 92: 5116 Det finns 2 punkter på x-axel
- Page 93 and 94: 5206 5207 5208a Sträckan = Hastigh
- Page 95 and 96: 5220 5223 5303a y= 3x−2 y= x+ −
- Page 97 and 98: 5314a P = (0,0) 1 } } 3 Δy k = 4
- Page 99 and 100: 5328 Genom R R ST ( −3,6) (2,
- Page 101 and 102: 5340a Enpunktsformen ger (5,4) k
- Page 103 and 104: 5354e − 3x+ 3y− 15= 0 3y= 3x+ 1
- Page 105 and 106: 5366 VL HL y = 5 −2 x (1.1,2.7)
- Page 107 and 108: 5375 2 y = 2 ax+ a (1,8) x y 2 8=
- Page 109 and 110: 5407a ⎧4x− 3z = 6 ⎨ ⎩z −
- Page 111 and 112: 5420c ⎧2m− 5n= 1 ⎨ ⎩3m+ n=
- Page 113 and 114: 5424a ⎧6 − ( x+ y+ 1) = x ⎨
- Page 115 and 116: 5429a ⎧x = 3 ⎪ ⎨2x+ y = 5 ⎪
- Page 117 and 118: 5431a ⎧x+ 3y− z = 4 ⎪ ⎨2x+
- Page 119 and 120: 5453 Antagande se figur LÖSNINGAR
- Page 121 and 122: LÖSNINGAR DEL B 120
4304d<br />
2 2<br />
4 x(3x − 1)(3 + x )<br />
2 4 2<br />
4 x(9x + 3x −3 −x<br />
)<br />
36x + 12x −12x−4x x + x − x<br />
3 5 3<br />
5 3<br />
12 32 12<br />
4304g<br />
5 x(3x− 2)(2x+ 3)<br />
2<br />
5 x(6x + 9x−4x−6) 3 2 2<br />
30x + 45x −20x −30x<br />
3 2<br />
30x + 25x −30x<br />
4307a<br />
2<br />
( a + 5)<br />
a + 2⋅a⋅ 5+ 5<br />
2<br />
a + 10a+ 25<br />
2 2<br />
4307d<br />
2<br />
(3x+ 4 y)<br />
(3 x) + 2⋅3x⋅ 4 y+ (4 y)<br />
2 2<br />
9x + 24xy+ 16y<br />
2 2<br />
4308a<br />
( x+ 5) + ( x−5)<br />
2 2<br />
2 2 2 2<br />
( x + 2⋅x⋅ 5+ 5 ) + ( x −2⋅x⋅ 5+ 5 )<br />
2 2<br />
( x + 10x+ 25) + ( x − 10x+ 25)<br />
2<br />
2<br />
x + 10x<br />
+ 25 + x −10x<br />
+ 25<br />
2<br />
2x+ 50<br />
LÖSNINGAR DEL B<br />
4304e<br />
<br />
0,5(10x + 3)(3−10 x)<br />
0,5(3 + 10 x)(3−10 x)<br />
2 2<br />
0,5(3 + (10 x)<br />
)<br />
2<br />
0,5(9 + 100 x )<br />
2<br />
4,5 − 50x<br />
4304h<br />
<br />
⎛ a ⎞⎛ a ⎞<br />
10⎜1− ⎟⎜1+ ⎟<br />
⎝ 10 ⎠⎝ 10 ⎠<br />
⎛ a ⎞⎛ a ⎞<br />
10⎜1+ ⎟⎜1− ⎟<br />
⎝ 10 ⎠⎝ 10 ⎠<br />
2<br />
⎛ 2 ⎛ a ⎞ ⎞<br />
10 1<br />
⎜ ⎝<br />
− ⎜ ⎟<br />
⎝10 ⎠ ⎟<br />
⎠<br />
2<br />
⎛ a ⎞<br />
10⎜1−⎟ ⎝ 100 ⎠<br />
4307b<br />
2<br />
( x − 8)<br />
x −2⋅x⋅ 8+ 8<br />
2<br />
x − 16x+ 64<br />
2 2<br />
4307e<br />
2<br />
( a+ 0,5 b)<br />
a + 2⋅a⋅ 0,5 b+ (0,5 b)<br />
2 2<br />
a + ab+ 0,25b<br />
2 2<br />
4308b<br />
( ) 2<br />
4304 f<br />
x y x y<br />
40((5 x ) − ( y ) )<br />
4 4<br />
40(25 x − y )<br />
4 4<br />
1000x − 40y<br />
40(5<br />
2<br />
+<br />
2<br />
)(5<br />
2<br />
−<br />
2<br />
)<br />
2 2 2 2<br />
2<br />
a<br />
10⋅1−10⋅ 100<br />
2<br />
10 a<br />
10⋅1− ⋅<br />
1 10 ⋅10<br />
2<br />
a<br />
10 −<br />
10<br />
4307c<br />
2<br />
( x+ 3 y)<br />
x + 2⋅x⋅ 3 y+ (3 y)<br />
2 2<br />
x + 6xy+ 9y<br />
2 2<br />
71<br />
4307 f<br />
2 2 2<br />
(4x + 5 y )<br />
(4 x ) + 2⋅4x ⋅ 5 y + (5 y )<br />
4 2 2 4<br />
16x + 40x y + 25y<br />
2 2 2 2 2 2<br />
2<br />
(2 a+ b) − 2a−b<br />
2 2 2 2<br />
((2 a) + 2⋅2 a⋅ b+ b ) −((2 a) −2⋅2 a⋅ b+ b )<br />
2 2 2 2<br />
(4a + 4 ab+ b ) −(4a − 4 ab+ b )<br />
4a<br />
2<br />
8ab<br />
2<br />
+ 4ab + b<br />
2<br />
− 4a<br />
2<br />
+ 4ab − b
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