6-mavzu. birhad va ko'phad

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f.o’roqov +99899.014.65.61 17 birhad va ko’phad. 1. sonli ifoda va uning qiymati. 2. algebraik ifoda va uning qiymati. 3. qavslarni ochish va qavsga olish. 4. birhad va uning standart shakli. 5. birhadning darajasi va birhadni darajaga ko’tarish. 6. birhadni birhadga ko’paytirish. 7. ko’phad va uning darajasi. 8. o’xshash hadlar. 9. birhadni ko’phadga ko’paytirish. 10. ko’phadni ko’phadga ko’paytirish. 11. ko’phadni birhadga va ko’phadga bo’lish. 12. umumiy ko’paytuvchini qavsdan tashqariga chiqarish. 1. sonlar va amallardan (qo‟shish, ayirish, ko‟paytirish, bo‟lish, daraja) tuzilgan ifodaga sonli ifoda deyiladi. hisoblashdan olingan natijaga sonli ifodaning qiymati deyiladi. m: 3∙2 2 +4 bu sonli ifoda; 16 uning qiymati. 2. sonlar, harflar va amallardan tuzilgan ifodaga algebraik ifoda deyiladi. m: 3a 4 +7bc. berilgan sonlarni harflar o‟rniga qo‟yib hisoblashdan olingan natijaga algebraik ifodaning qiymati deyiladi. m: 3a 4 +7bc, bunda a=1, b=–1, c=4 3∙1 4 +7∙(–1)∙4=–25 3. qavslarni ochishda qavs oldida minus “–” ishorasi turgan bo‟lsa qavs ichidagi barcha …

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d birhadni darajaga ko‟tarishda birhadning har bir hadini shu darajaga ko‟tarish kerak. m: m∙(4a 6 ∙b 3 ∙m 3,5 ) 4 = m∙4 4 a 24 ∙b 12 ∙m 14 6. birhadni birhadga ko‟paytirishda koeffitsiyentlar (sonlar) alohida, harflar alohida ko‟paytiriladi. m: 3abc 4 ∙12ma 2 b=36a 3 b 2 c 4 m 7. bir nechta birhadlarning algebraik ifodasiga ko’phad deyiladi. m: a4 b+7c–3mn 5 . ko’phadning darajasi deganda ko‟phadni tashkil etuvchi eng katta darajali birhad tushuniladi. m: 7a 6 m 4 –24a 7 b 8 c+3abcde [d]=7+8+1= 16–darajali ko‟phad. 10 16 5 8. ko‟phaddagi birhadlarning harfiy qismlari aynan bir xil bo‟lsa, bu hadlar o’xshash hadlar deyiladi. o‟xshash hadlarning faqat koeffitsiyentlari soddalashadi (harflari o‟zgarmaydi). m: 5ab 3 +4ab+3ab 3 +12ac 2 –7ab 3 =ab 3 +4ab+12ac 2 m: –(2ab 2 –ab+b)+3ab 2 –4b–(5ab–ab 2 ) = –2ab 2 +ab–b +3ab 2 –4b–5ab +ab 2 = 2ab 2 –4ab –5b 9. birhadni …

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8b 4 c 6 y+16b 5 c 5 y 8 = –4b 4 c 5 y∙(7c–4by 7 ) f.o’roqov +99899.014.65.61 18 daraja va uning xossalari: a 0 =1, 5 0 =1 a 1 =a, 15 1 =15 a –n 2 2- 3 1 3 , 1  na , 4 9 3 2 -2       a m ∙a n =a m+n , 5 3 ∙5 6 =5 9 a m :a n =a m–n , 5 3 :5 10 =5 –7 (a m ) n =a m∙n , (3 4 ) 5 =3 20 (a∙b) m =a m ∙b m , (3∙2) 2 =3 2 ∙2 2 (a m ∙b n ) k =a mk ∙b nk , (3 –5 ∙2 3 ) –2 =3 10 ∙2 –6 4 44 8 3 8 3 ,           …

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‟indining kubi: (a+b) 3 =a 3 +3a 2 b+3ab 2 +b 3 = = a 3 +3ab(a+b)+b 3 ayirmaning kubi: (a–b) 3 =a 3 –3a 2 b+3ab 2 –b 3 = = a 3 –3ab(a–b)–b 3 a 4 –b 4 =(a 2 –b 2 )(a 2 +b 2 )= =(a–b)(a+b)(a 2 +b 2 ) a 4 +a 2 +1 = =(a 2 +a+1)(a 2 –a+1) (a+b+c) 2 = a 2 +b 2 +c 2 +2ab+2ac+2bc (a+b–c) 2 = a 2 +b 2 +c 2 +2ab–2ac–2bc eslatma: agar ikki hadning faqat bittasini ishorasini o‟zgartirsak qo’shma sonlar hosil bo‟ladi. m: a+b ga qo‟shma son a–b yoki –a+b. 7–x ga qo‟shma son 7+x yoki –7+x m: 1) 8 42 3 3226 8 42 4 2 3 2 26 4 2 4 2 3 2 4 9 16 3 2564 9 2 3 4 1 2 4 1 2 3 4 1 y ba …

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z–2y) – (3z–2y) 3 = –3(3z–x)(x–2y)(3z–2y) 2) ayniyatdan a ni toping. (ax+2y)(3x+by)=cx2+7xy+y2 yechish: bu tenglik ayniyat bo‟lishi uchun: chap tomondagi x2 oldidagi son o‟ng tomondagi x2 oldidagi songa teng bo‟lishi kerak; chapdagi xy oldidagi son o‟ngdagi xy oldidagi songa teng bo‟lishi kerak; ozod sonlar ham xuddi shunday. 3ax2+abxy+6xy+2by2=cx2+7xy+y2 , 3ax2+(ab+6)xy+2by2=cx2+7xy+y2 5,0 2a ,15,0 6c ,23 12 76 3               b a c b ab ca j: a=2 3) xy+xz+yz=16 bo‟lsa, x2+y2+z2 ifodaning eng kichik qiymatini toping. yechish: 16 : 16 2yz22)2( 2 2 2 4)( 4)( 4)( 2 2 2 2 mavzusidan nazariyasilinish bo' 222 222 22 22 22 2 2 2 j zyx xzxyzyx yzzy xzzx xyyx yzzy xzzx xyyx yzzy xzzx xyyx xy yx                      …

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f.o’roqov +99899.014.65.61 17 birhad va ko’phad. 1. sonli ifoda va uning qiymati. 2. algebraik ifoda va uning qiymati. 3. qavslarni ochish va qavsga olish. 4. birhad va uning standart shakli. 5. birhadning darajasi va birhadni darajaga ko’tarish. 6. birhadni birhadga ko’paytirish. 7. ko’phad va uning darajasi. 8. o’xshash hadlar. 9. birhadni ko’phadga ko’paytirish. 10. ko’phadni ko’phadga ko’paytirish. 11. ko’phadni birhadga va ko’phadga bo’lish. 12. umumiy ko’paytuvchini qavsdan tashqariga chiqarish. 1. sonlar va amallardan (qo‟shish, ayirish, ko‟paytirish, bo‟lish, daraja) tuzilgan ifodaga sonli ifoda deyiladi. hisoblashdan olingan natijaga sonli ifodaning qiymati deyiladi. m: 3∙2 2 +4 bu sonli ifoda; 16 uning qiymati. 2. sonlar, harflar va amallardan tuzilgan ifodaga algebraik ifoda dey...

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