Gtal n Rumt 1VWO l 2 MA2N Hoostuk 8 Utwrknn m / 2
Gtal n rumt 1VWO l 2 - Hst 8 8.1 Hrln 1a 6a + 2a = 8a 7p p = 6p 3p + 3q = kan nt 4a 7 = 28a 2a 5a = 10a² j 2 3a = 6a 3a + 2 + 5a = 8a + 2 2a 5 + 7 a = a + 2 8a + 3a + a = 12a 2a + 3 + 2a 4 = 2a 5 3a = 15a 6 2a = 12a 5 3a + 6 2a = 27a 3a 5 2 + 10 3 = 40 5 2 + 3 = 7 8 2 5 3 = 31 5a 2 2a = 8a 5a 3 2a = 15a + 2a 8a 3 5 3a = 9a 4a 3 2x + 4 2 x = 14x 5 3y 8 2y = y 5x 2y 15x y = 5xy 3x 2z 5x 2y = 6xz 10xy 4 2x 8 6 = 8x 48 4 2x 8x 3 = 16x 5a 2 3x + 5 2 x = 16x 2 + 3x + 5 + 2 x = 5x + 7 2 3x + 5 + 2 x = 8x + 5 3 2x + 5x 2 x = 3x 3 + 2x + 5 2 x = 2 3 2x 5 2 x = 16x 6a 3 4a + 5 2a = 22a 3a 4 + 2a 3 = 18a 3a + 4 + 2a + 3 = a + 7 3a 3 + 2a 3 = 3a 3a 3 + 2a 3 = a 6 3a 3 + 2a 3 = 3a 7a 16a = 4a + 12a 1 2 8xy = 2 xy 5 xy 3 3 16a = 17a a 1 16a = a 64a 4 18xy = 2x 3y + 3x 4y 8xy = 2x 3y + x 2y 8 15a 3a = 12a 2a 3 + 3a 2 = 12a 3 4a = 12a 5a 4 2a 4 = 12a 1 1 8a = 12a 2 9a 2 + 6a 5 = 12a a 12 = 12a 10a + 2a = 12a 4a 2 + a 2 + 2a = 12a 1 2 2 a + 9 a = 12a 3 3 9a 5x 3y 3x + 2y = 15xy 3x + 2y 5 3y 3x 2y = 15y + 6xy 5x + 3y 3x 2y = 2x + y 6a 2 2 a + 5a 2 = 20a 3a 2 2 a + 5a 2 = 3a 2 8a 3a 2 2 a + 5a 2 = 7a 6
10a D pottn n oosjs op plank 4 vattn 2a + 3 kraln. D kast vat n totaal 12a + 5 kraln. Ht totaal aantal kraln s 5a + 3 3a + 2 = 2a + 5 kraln. 11a 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 5, 7, 12, 19, 31, 50, 81, 131, 212, 343, 555, 898, Ht jzonr aan rj van Fona s at rj nt j t jr 1. (Soms laat mn rj van Fona ook wl nnn mt 0,1,1,2.) a,, a +, a + 2, 2a + 3, 3a + 5, 5a + 8, 8a + 13, 13a + 21, 21a + 34, a +, 2a, 3a +, 5a +, 8a + 2, 13a + 3, 21a + 5, 34a + 8, a, a +, 2a, 3a +, 5a +, 8a + 2, 13a + 3, 21a + 5, a 2, 2a, a, 3a, 4a, 7a, 11a 2, 18a 3,
Gtal n rumt 1VWO l 2 - Hst 8 8.2 Haakjs wwrkn 12 D omtrk van rtok kun j srjvn als a + + a + o 2a + 2 o 2(a + ). 13a Totaal aantal plantn = 7 5 Aantal plantn onr nt = 4 5 Aantal plantn nt onr nt = 3 5 Ht totaal aantal plantn s ljk aan t aantal plantn onr t nt plus t aantal plantn nt onr t nt. Dus 7 5 = 3 5 + 4 5 14a 5(a + ) = 5a + 5 8(2a + ) = 16a + 8 5a(2 + ) = 10a + 5a 3p(x + 3) = 3px + 9p 1½(4x + 2y) = 6x + 3y 8p(2r + s) = 16pr + 8ps 15a 1 6 a(3 + ) = 18a+ 3a 1 3 1 ( a + 6) = a + 2 1 2 3 4 4 2 p(4q + 8 s) = 2pq + 4ps 3 1 7 a( + 14 ) = 7a + 12 a 5 a(2 + 1 ) = 10a + 7 a 2 1 pq(3r + 1 s) = 2 pqr + pqs 1 1 2 2 3 2 16a 4(a + 3) + 2a = 4a + 12 + 2a = 6a + 12 5(x + 2y) + 3y = 5x + 10y + 3y = 5x + 13y 5(a + 2) + 3(3a + ) = 5a + 10 + 9a + 3 = 14a +13 4(2x + 5y) + 5(x + 5y) = 8x + 20y + 5x + 25y = 13x + 45y 17a y = 8(x + 6) = 8x + 48 T = 4(2a + 3) = 8a + 12 y = 5(x + 1) + 3(2x + 6) = 5x + 5 + 6x + 18 y = 11x +23 A = 5(2 + 3) = 10 + 15 18a 4(x + 2y) = 4x 8y 4(x 2y) = 4x 8y 4(x 3) = 4x + 12 4(2x + 8) = 8x 32 (2x 3) = 2x + 3 (2x + 3) = 2x 3 19a 3a(2 + ) = 6a 3a 1 1 1 4( 4 q 3r) = q+ 12r 5a(3 ) = 15a 5a ( 3p q) = 3p + q 2p(3q 1) = 6pq + 2p 2 1 1 2 ( 1 ) = 3 5 2 15 20a 3(a + 2) 6a = 3a + 6 5(a 2) + 6a = a + 10 5(a 2) + 3(2a ) = 11a 13 8(a ) 5(a 3) = 3a 8 + 15 2a (5 + 2a) = 5 3a( 1) 3a = 3a + 3a 3a = 3a
21a 7(x + y) 2(3x y) + 5x = 7x + 7y 6x + 2y + 5x = 6x +9y 3p p(q + 3) + q(2 p) = 3p pq 3p + 2q pq = 2q 2pq 3(a 6) 2a a( 4) = 3a + 18 2a a + 4a = a + 18 3a 8y 2x(y +7) y(x 8) = 8y 2xy 14x xy + 8y = 16y 3xy 14x 22a 3x 2y + x(y 5) = 8x 2y + xy 5p(q + 3) 2p 3q = 11pq + 15p 3a 7 + 2a(3 5) + (1 a) = 21a + 6a 10a + a = 10a + 6a + 2x(5y 2) 5x 2y = 4x 2p(q 1) (1 2p) = 2pq 2p 1 + 2p = 2pq 1 3p 2q q(6p + 1) = 6pq 6pq q = q 23 Blauw: Opprvlakt = x(y + 3) = xy + 3x Omtrk = 2(y + 3) + 2 x = 2y + 2x + 6 Gl: Opprvlakt = 7(p + 5) = 7p + 35 Omtrk = 2(p + 5) + 2 7 = 2p + 24 Gron: Opprvlakt = 2p(q ) = 2pq 2p Omtrk = 2(q ) + 2 2p = 2q 2 + 4p 24a Er zttn a 16 kraln n pot. Franka rjt (p 2) 3 = 3(p 2) = 3p 6 klomtr. Wllk rjt 12 a klomtr. Japp krjt 4(p + 5) = 4p + 20. Flors was 5p 5 jaar. Tomas zjn var s 4(x 3) = 4x 12 jaar. 25a J krjt (x +2) 3 = 3(x + 2) = 3x + 6 J krjt 4(a + 5) 4a = 20 26a Lnt = 4(a + 3) + 5(2a + 4) = 4a + 12 + 10a + 20 = 14a + 32 Lnt = 8(a + 3) + 3(2a + 4) + 7(3a + 8) = 8a + 24 + 6a + 12 + 21a + 56 = 35a + 92 Lnt = 32a + 96 3(a + 3) = 32a + 96 3a 9 = 29a +87 Lnt = 40a + 120 2(2a + 4) 4(3a + 8) = 40a + 120 4a 8 12a 32 = 24a + 80 27a - Ht kozn tal kun j truvnn 24 van utkomst a t aln. (x + 6) 4 3 x = 4(x + 6) 3x = x + 24 D utkomst s us 24 mr als t kozn tal. Nm n tal n atn, vrmnvul t mt 2, tl r 5 j op n vrmnvul z utkomst mt 4. Nu van t rsultaat 8 kr t oorspronkljk tal ra aln. D utkomst s altj 20. Brknn: (2x + 5) 4 8 x = 4(2x + 5) 8x = 8x + 20 8x = 20
28 I Is just, ljkt r op ornl rl. II Is just,.p.v. vrmnvuln nu ln. III Is nt just, 12 : (2 + 4) = 2 n 12 : 2 + 12 : 4 = 9 IV Is nt just, 10 (3 + 4) = 3 n 10 3 + 10 4 = 13 V Is nt just, 20 (15 : 3) = 100 n (20 15) : (20 3) = 5 VI Is just, s n utrn van rl a( + ) = a + a VII Is just, ook wl kn oor rl: ln oor n ruk s vrmnvuln mt t omkr
Gtal n rumt 1VWO l 2 - Hst 8 8.3 Matn 29a Woutr t an 2 2 2 2 2 2 = 64 snpprs. Ik sat at j an ook 6 kr kunt surn, oout 7 kr want anrs krj j tvl snpprs om n één kr oor t surn. 30a 5³ = 5 5 5 = 125 5³ sprk j ut als vj tot mat 3. In 5³ s 5 t rontal n 3 xponnt. 31a 2 5 = 32 6 3 = 216 10 5 = 100000 2 6 = 64 1 7 = 1 0 8 = 0 1 9999 = 1 0 2000 = 0 32a 5 4 = 5 5 5 5 = 625 3 4 = 81 10 3 = 1000 33a 8 = 2 3 81 = 9 2 125 = 5 3 64 = 4 3 64 = 2 6 64 = 8 2 1000 = 10 3 27 = 3 3 169 = 13 2 j k l 1 = 1 7 32 = 2 5 0 = 0 11 34a Exponnt 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 utkomst 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 2 19, 2 23 n 2 55 nn op n 8. 2 4, 2 8, 2 12, 2 16, 2 20, t. 2 94 nt op n 4. ( 2 94 = 19807040628566084398385987584 ) 9 23 = 8862938119652501095929, nt us op n 9. 35-36a 2 3 5 = 40 2 5 3 = 250 2 3 5 3 = 8 125 = 117 (5 2) 4 + 2 = 81 + 2 = 83 (3 4) 2 8 = 136 3 7 2 8 = 139 2 5 5 2 = 32 25 = 7 (2 3 + 3) 2 = 11 2 = 121 j k l 12 6 2 = 12 36 = 24 6 2 : 3 2 = 36 : 9 = 4 5 (3 2) 3 = 5 5 3 2 3 = 5 24 = 19 37a 96 = 2 2 2 2 2 3 = 2 5 3 360 = 2 2 2 3 3 5 = 2 3 3 2 5 550 = 2 5 5 11 = 2 5 2 11 875 = 5 5 5 7 = 5 3 7 4410 = 2 3 3 5 7 7 = 2 3 2 5 7 2 18000 = 2 2 2 2 3 3 5 5 5 = 2 4 3 2 5 3 38a 2 2 2 2 = 16 2 2 2 2 = 16 Ht rst tal 2 2 2 2 = 16 s vr mat van 2.
39a ( 2) 4 = 16 2 4 = 16 ( 3) 3 = 27 3 3 = 27 5 + ( 2) 4 = 21 5 2 4 = 11 ( 1) 6 3 3 = 26 12 ( 2) 3 = 20 40a ( 4) 6 s pos. ( 11) 19 s n. ( 5) 7 s n. ( 1,5) 12 s pos. ( 0,3) 9 s n. ( 7) 10 s pos. ( 1) 10 s pos. ( 12) 15 s n. Rl: Nat rontal n vn xponnt an s utkomst post; Nat rontal n onvn xponnt an s utkomst nat. D rl lt nt voor 7 4 want t s nt vr mat van 7 41a 5 ( 2) 4 = 5 16 = 21 5 2 ( 2) 5 = 25 32 = 7 (5 2) 4 = ( 10) 4 = 10000 5 (2 3)6 = 5 1 = 4 3 4 + ( 3) 4 = 81 + 81 = 0 1 4 + ( 1) 5 = 1 + 1 = 2 32 : ( 2) 5 = 32 : 32 = 1 6 3 2 ( 3) 2 = 216 2 9 = 216 18 = 198 5 2 3 2 ( 2) 3 = 25 9 8 = 25 72 = 47
Gtal n rumt 1VWO l 2 - Hst 8 42a 2,3 2,3 2,3 2,3 = 27,9841 2,3 4 = 27,9841 D utkomstn zjn ljk! 8.4 Matn n rknman 43a 5,6 3 = 175,62 0,95 4 5,2 = 4,24 ( 2,6) 4 1,7 3 = 40,78 0,58 2,5 3 ( 1,4) 3 = 11,81 (3,7 0,27) 5 = 1,00 (4,7 2,8) 3 : ( 1,8) 4 = 0,65 44a 3 4 (1 7) 4,16 3 2,1 8 4 = = 0,61 1, 5 3 4 1 3 1 4 (2 3) + ( 1 6) = 14,56 3 3-5 : ( ) 211,64 4 = 7 5 ( 2,3) 100 = 10,48 2 4 = 1, 77 4 3 1,3 5 2,8 45a In 2003 wr r 50000 0,7 = 35000 ton aanvor n n 2004 was at 35000 0,7 = 24500 ton 2008 s 6 jaar na 2002, j mot an us 50000 0,7 0,7 0,7 0,7 0,7 0,7 utrknn. Dt s tzl als 50000 0,7 6 = 5882,45 ton. Dt s 50000 5882,45 = 44117,55 ton mnr als n 2002!!!! 46a Joan Ptrs a 16 ouovrrootours ( 2 4 = 16 ). Ht aantal voorours van 10 nrats tru s 2 10 = 1024 1500 s 510 jaar ln. Dat zjn 510 : 25 20 nrats ln. Dus 2 20 = 1048576 voorours. - 2010 1200 = 810 810 : 25 32 nrats 2 32 = 4294967296 voorours 47a 10 5 = 100000 Er staan 5 nulln n t antwoor. Bj 10 9 krj j 9 nulln. En mljon t 6 nulln. 1 mljon = 1000000 = 10 6 1 mljar = 1000000000 = 10 9 48a 480000 = 4,8 10 5 900000000000 = 9 10 11 180000000 = 1,8 10 8 152500 = 1,525 10 5 158 = 1,58 10 2 5390 = 5,39 10 3 49a En volwassn olant kan 6,9 10 6 ram wn. En uw uurt jna 3,16 10 9 sonn. In n mnsnlvn slaat t art onvr 2,8 10 9 kr. Ht aantal arn op n oo s onvr 1,4 10 5. D lauw kra lt n aar lvn 1,75 10 6 rn. 50a 5,7 10 5 = 570000 1,236 10 4 = 12360 4,28 10 5 = 428000
51 4.28 10 4 = 42800 1.732 10 11 = 173200000000 8.3 10 9 = 8300000000 52a 2 58 = 2,88 1017 5,3 28 = 1,90 10 20 1,8 3,7 25 = 2,89 10 14 2,5 14 3,1 9 = 9849526793 53a (32 10 6 ) : (25 10 3 ) = 1280 rvn passn op USB-stk. (80 10 9 ) : (650 10 6 ) = 123,0769. Er passn us 123 -roms op vast sj. 54a 2 4 1 = 16 1 = 15 1 + 2 + 4 + 8 + 16 = 31 2 5 1 = 32 1 = 31 Voor rst 10 vakjs: 2 10 1 = 1024 1 = 1023 raankorrls. Voor rst 20 vakjs: 2 20 1 = 1048576 1 = 1048575 raankorrls. Voor t l saakor warn at 2 64 1 = 1,845 10 19 raankorrls. (1,845 10 19 ) : 180000000 = 1,025 10 11 waons van 10 mtr no. Er aan 100 waons n n klomtr, us 1,025 10 11 : 100 = 1,025 10 9 klomtr. 1,025 10 9 : 40000 = 2562500 D trn zou us 2562500 kr omtrk van aar worn!! Sssa vro 1,845 10 19 : 18000000 = 1,025 10 12 ton raan Dat s 1,025 10 12 : 10 9 = 1025 mljar ton raan. Ht uurt us 1025 jaar voorat aan sn wns van Sssa s volaan. 55a 0,00000052 : 10000 = 5,2 10 11 komt n t vnstr van rknman. 1 12 = 10 komt r n t vnstr. 12 10 56a 0,0037 = 3,7 10 3 0,000000812 = 8,12 10 7 0,07183 = 7,183 10 2 0,00007 = 7 10 4 0,12 = 1,2 10 1 81200 = 8,12 10 4 57a 0,0000031 = 3,1 10 6 0,0000000092 = 9,2 10 9 0,000000001 = 10 9 58a 3,67 10 6 = 0,00000367 1,8 10 12 = 0,0000000000018 9,318 10 2 = 0,09318 59a 0,013 12 = 2,33 10 23 8,7 0,12 24 = 6,92 10 22 0,21 8 0,035 7 = 2,43 10 16 0,32 20 = 1,27 10 10 3 7 30 = 9,13 10 12 18 1 6 :8,5 = 3,07 10 7 21
60a 5x 2x = 10x 2 4x x 3x = 12x 3 2a 5a 3a a = 30a 4 Gtal n rumt 1VWO l 2 - Hst 8 5p p p = 5p 3 4x x = 4x 2 2 2 = 4 4 8.5 Matn n lttrs 61a p 3 p 4 = p 7 p 5 p 3 = p 8 62a 5 8 = 13 x x 4 = x 5 x 3 x 5 x = x 9 x 5 x x x 2 = x 9 p 8 p 9 = p 17 p p p = p 3 63a 2a 5 3a 7 = 6a 12 8a 6 3a = 24a 7 4m 6 2m 7 = 8m 13 y 3 2y 9 = 2y 11 3p 4 2p 12 = 6p 16 q 6 3q = 3q 7 64-32a 13 54a 13 96a 20 4a 7 8a 6 18a 5 3a 8 8a 8 12a 12 2a 4 2a 3 4a 3 6a 3a 4 a 4 2a 5 4a 3 3a 9 a 3 2a a 2 4a 2 3a a 3 a a 3 2a 2 2a 1 a 1 2 8 65a 5x 3 2x 4 x = 10x 8 a 3 a 6 2 = a 7 5 x 2 y 3 x 5 y 2 = x 7 y 5 2a 3 5a 3 2 = 10a 4 8 3p 6 3p 6 = 9p 12 6x 2 3y 2y 5 2x = 72x 3 y 6 66a Luuk t natuurljk ljk want j mot j n vrmnvuln xponntn j lkaar optlln. 2 6 2 3 = 2 9 3 8 3 11 = 3 19 4 4 8 = 4 9 67a Inou = zj zj zj = a a a = a 3 Opprvlakt rnsvlak = a a = a 2 Opprvlakt kuus = 6 a 2 = 6a 2 68a 7a 3 + 5a 3 = 12a 3 3a 2 9a 2 = 6a 2 4a 4 a 4 = 3a 4 8 8 8 = 7 8 5 5 5 = 4 5 12 2 + 3 2 = 15 2 a 2 + 2a 2 = 3a 2 x 2 + x 2 = 2x 2 2x 2 + 8x 2 = 10x 2 69a 8a 6a = 2a 13p 2 + p 2 = 14p 2 5a 3 + 5a 3 = 10a 3 6x 6 7x 6 = x 6 2x 2 + 8y 2 kan nt 8a 2 7a 2 = a 2 6a 2 10a kan nt 5x 2 5x 2 = 0 7p 3 + 41p 3 = 48p 3 70a 3x 5 + 2x 5 = 5x 5 3x 5 2x 5 = 6x 10 5x 3 2x 5 kan nt 5x 3 2x 5 = 10x 8 x 3 + 2x 3 = 3x 3 x 3 2x 3 = 2x 6
71a 12x 6 = 8x 6 + 4x 6 12x 6 = 6x 4 2x 2 12x 6 = x 12x 5 12x 6 = 15x 6 3x 6 12x 6 = 2x 4 6x 2 12x 6 = 3x 4x 5 72 2a 5 9a 3 = 3a 8 + 21a 8 = 87a 8 69a 8 = 6a 3a 7 = 5a 8 + 13a 8 = 10a 8 28a 8 = 18a a 7 = 8a 8 + 10a 8 = 19a 8 a 8 = 6a 6 3a 2 = 73a a 3 a 2 + 3a 5 = 4a 5 2a 4 a 2 + 5a 3 a 3 = 7a 6 7a 8 + 2a 2 3a 6 = 13a 8 8a 2 3a 5 2a 4 3a 3 = 30a 7 74a 3a 2 (a 4 + 2a) = 3a 6 + 6a 3 5a(a 3 2a) = 5a 4 10a 2 3a 2 (a 2) = 3a 3 + 6a 2 a 3 (a 5 a 4 ) = a 8 a 7 a 3 (2a 1) + a 3 = 2a 4 a 3 + a 3 = 2a 4 a 2 (a 3 2a) + a 4 (a 1) = a 5 2a 3 + a 5 a 4
75a Gtal n rumt 1VWO l 2 - Hst 8 2x 2x 2x = 8x 3 2x 2x 2x 2x = 16x 4 Ja (2x) 4 = 2x 2x 2x 2x 8.6 Hrln van Matn 76a (a) 7 = a 7 7 (pq) 12 = p 12 q 12 ( 4x) 2 = 16x 2 (a) 9 = a 9 9 9 ( 3a) 3 = 27a 3 ( 2pq) 4 = 16p 4 q 4 (4xy) 2 = 16x 2 y 2 (10a) 3 = 1000a 3 ( a) 3 = a 3 3 77a (3a) 2 ( 2a) 3 = 9a 2 8a 3 = 72a 5 3 (3) 3 = 27 6 ( 4) 3 ( ) 5 = 64 8 ( 2a) 6 (5a) 2 = 64a 6 25a 2 2 = 1600a 8 2 (3xy) 4 xy 2 = 81x 4 y 4 xy 2 = 81x 5 y 6 ( 2) 3 3 4 = 3 3 4 = 3 7 78 1 (4a) 2 = 16a 2 7 16a 2 2 ( 4a) 2 = 16a 2 8 16a 2 3 4a 2 9 (2a) 2 = 4a 2 4 8a 2a = 16a 2 10 4a 4a = 16a 2 5 2a 2a = 4a 2 11 ( 2a) 2 = 4a 2 6 (4a) 2 = 16a 2 12 4a 2 D orjs 1, 2, 7 komn op tzl nr. D orjs 3 n 5 n orjs 4, 6, 8 n 10 n vrr orjs 9, 11 n 12 komn tlkns op tzl nr. 79a Inou kuus I = 4a 4a 4a = 64a 3 Opprvlakt kuus I = 6 4a 4a = 96a 2 Inou kuus II = 8a 8a 8a = 512a 3 Opprvlakt kuus II = 6 8a 8a = 384a 2 512a 3 : 64a 3 = 8 D nou van kuus II s 8x zo root als nou van kuus I. 384a 2 : 96a 2 = 4 D opprvlakt van kuus II s 4 x zo root als opprvlakt van kuus I. 80a (5 2 ) 3 = 5 6 (3 2 ) 4 = 3 8 (10 3 ) 4 = 10 12 (2 2 ) 2 = 2 4 (6 6 ) 2 = 6 12 (7 4 ) 4 = 7 16 81a (a 2 ) 6 = a 12 ( 5 ) 2 = 10 (a 2 ) 3 = a 3 6 ( 8 ) 2 = 16 (a 7 ) 4 = a 28 (p 6 ) 8 = p 48 a 3 (a 9 ) 2 = a 3 a 18 = a 21 x (x 12 ) 10 = x x 120 = x 121 (p 3 ) 4 (p 6 ) 3 = p 12 p 18 = p 30 82a (2a 2 ) 3 = 8a 6 ( 3a3)3 = 27a9 (a2)3 = a35 (x 3 y) 2 = x 6 y 2 ( 3a 2 ) 4 = 81a 8 4 (4a 2 2 ) 3 = 64a 6 6 (a 3 3 ) 4 = a 4 12 12 ( xy 6 z 5 ) 4 = x 4 y 24 z 20 (pq 3 ) 2 (p 6 q 3 ) 3 = p 2 q 6 p 18 q 9 = p 20 q 15 83a x x 7 12 9 4 x 3 x = 11 x x = 2 18x 2x 9x = 7 15x 8 3x 8 = 5
84a a 12 8 3 5 9 4 a 3 4 a = 3 21a 3a 7a = 2 2 18 9 12 a 12 a = 2 85a a 8 5 a 3 a = a8 a 3 = a 11 a 8 + a 3 a 2 = a 8 + a 5 (a 3 ) 8 = a 24 8a 3 3a 8 = 24a 11 (3a 8 ) 3 = 27a 24 86a (2a) 3 + 4a 3 = 8a 3 + 4a 3 = 12a 3 (2a 2 ) 3 + (3a 3 ) 2 = 8a 6 + 9a 6 = 17a 6 4a 3 2a 5 + (3a 4 ) 2 = 8a 8 + 8a 8 = 16a 8 2x 3 x + ( 3x 2 ) 2 = 2x 4 + 9x 4 = 7x 4 ( 5x 4 ) 3 + 5(2x 3 ) 4 = 125x 12 + 80x 12 = 205x 12 (5a 3 ) 2 3a 4 ( 2a 5 ) 2 = 75a 10 25a 10 =100a 10 87a 3a 3 2 2 + (4a) 2 a = 3a 3 2 +16a 3 2 = 19a 3 2 (2xy) 3 2(xy) 3 = 8x 3 y 3 2x 3 y 3 = 6x 3 y 3 3 3 6 4 (3 a) 9a 2 18 pq = = a = 6q 6 3 9a 9a 3pq 3(x 2 y) 3 (5xy) 2 x 4 y = 3x 6 y 3 25x 6 y 3 = 22x 6 y 3 a 2 (3a 4 5) + 5a 2 (2a 3 ) 2 = 3a 6 5a 2 + 5a 2 8a 6 = 5a 6 88a (5a 3 ) 4 3a 2 2a 4 + 18(a 9 ) 2 7(a 3 ) 2 (2a 4 ) 3 + ( 9a 9 ) 2 3333a 18 = 625a 12 6a 6 + 18a 18 7a 6 8a 12 + 81a 18 3333a 18 = 3750a 18 + 18a 18 + 56a 18 + 81a 18 3333a 18 = 6928a 18 7(a 3 4 ) 6 18(a 9 ) 2 (2 6 ) 4 + (3a) 2 (2a 3 4 ) 2 10(a 5 7 ) 2 + 5(a 3 3 ) 2 13(a 2 3 ) 6 = 7a 18 24 18a 18 16 24 + 9a 2 2 4a 6 8 10a 10 14 + 5a 6 6 13a 12 18 = 7a 18 24 + 288 a 18 24 360 a 18 24 + 65 a 18 24 = 0 4 3 6 3 3 3 3 3 5 5 3 3 9 ( 2 a) + 4( a) ( a) ( 3 a) 2( a) 2 12 4 4 6( a ) ( ) 64a + 4a a + 27a 2a = 24 16 6a 24 18 24 18 24 18 24 18 64a 4a 54a 6a = = = 24 16 24 16 6a 6a 24 18 9 3 15 15 15 9 9 9 2
Gtal n rumt 1VWO l 2 - Hst 8 Gmn Opavn