Davlat ixtisoslashtirilgan

= a³ + (ab² – ab²) + (a²b – a²b) + b³ = a³ + b³ .
Demak, a³ + b³ = (a + b)(a² – ab + b²) .
a² – ab + b² ifoda a va b lar ayirmasining chala kvadrati deyiladi.
Shunday qilib, ikki son kublarining yig‘indisi shu ikki son yig‘indisi bilan ular ayirmasining chala kvadrati ko‘paytmasiga teng.


a³ – b³ = (a –b)(a² + ab + b²)
tenglik kublar ayirmasi formulasi deyiladi.
(a – b)(a² + ab + b²) = a³ + a²b + ab² – a²b – ab² – b³ =
= a³ + (a²b – a²b) + (ab² – ab²) – b³ = a³ – b³ .
Demak, a³ – b³ = (a – b)(a² + ab + b²) .
a² + ab + b² ifoda a va b lar yig‘indisining chala kvadrati deyiladi.
Shunday qilib, ikki son kublarining ayirmasi shu ikki son ayirmasi bilan ular yig‘indisining chala kvadrati ko‘paytmasiga teng.


Kublar yig'indisi va ayirmasi formulalari ham ko'phadni ko'paytuvchilarga ajratishda qo'llaniladi.


Darsni mustahkamlash:
1. Qisqa ko‘paytirish formulalarini qo‘llab ifodalar qiymatini hisoblang:
a) 74² – 34² .
74² – 34² = (74 – 34)(74 + 34) = 40 · 108 = 4320 .
b) 55² – 45² .
55² – 45² = (55 – 45)(55 + 45) = 10 · 100 = 1000 .
c) 81,5² – 81,4² .
81,5² – 81,4² = (81,5 – 81,4)(81,5 + 81,4) = 0,1 · 162,9 = 16,29 .
d) 1001,5² – 1002,5² .
1002,5² – 1001,5² = (1002,5 – 1001,5)(1002,5 + 1001,5) =
= 1 · 2004 = 2004 .
2. Ko'paytuvchilarga ajrating:
a) 2a² + 2b² – 4ab .
2a² + 2b² – 4ab = 2(a² + b² – 2ab) = 2(a² – 2ab + b²) = 2(a – b)² .
b) 9m⁴n + 18m³n + 9m²n .
9m⁴n + 18m³n + 9m²n = 9m²n(m² + 2m + 1) = 9m³n(m + 1)² .
c) 9 + (– x² + 2xy – y²) .
9 + (– x² + 2xy – y²) = 9 – (x² – 2xy + y²) = 3² – (x – y)² =
= (3 – (x – y))(3 + (x – y)) = (3 – x + y)(3 + x – y) .
d) (a³ – b³) + (a – b)² .
(a³ – b³) + (a – b)² = (a – b)(a² + ab + b²) + (a – b)² =
= (a – b)(a² + ab + b² + a – b) .
e) (64p³ + 216q³) + 6q(16p² – 36q²) .
(64p³ + 216q³) + 6q(16p² – 36q²) =
= ((4p)³ + (6q)³) + 6q((4p)² – (6q)²) =
= (4p + 6q)((4p)² – 4p6q + (6q)²) + 6q(4p – 6q)(4p + 6q) =
= (4p + 6q)(16p² – 24pq + 36q²) + 6q(4p – 6q)(4p + 6q) =
= (4p + 6q)(16p² – 24pq + 36q² + 6q(4p – 6q)) =
= 2(2p + 3q)(16p² – 24pq + 36q² + 24pq – 36q²) =
= 2(2p + 3q)(16p² + (36q² – 36q²) + (24pq – 24pq)) =
= 2(2p + 3q)16p² = 32p²(2p + 3q) .
f) y⁶ + y⁵ + y⁴ + 2y³ + y² + y + 1 .
y⁶ + y⁵ + y⁴ + 2y³ + y² + y + 1 = y⁶ + y⁵ + y⁴ + y³ + y³ + y² + y + 1 =
= (y⁶ + y⁵) + (y⁴ + y³) + (y³ + y²) + (y + 1) =
= y⁵(y + 1) + y³(y + 1) + y²(y + 1) + (y + 1) =
= (y + 1)(y⁵ + y³ + y² + 1) = (y + 1)((y⁵ + y³) +(y² + 1)) =
= (y + 1)(y³(y² + 1) +(y² + 1)) = (y + 1)(y² + 1)(y³ + 1) =
= (y + 1)(y² + 1)(y + 1)( y² – y + 1) =
= ((y + 1)(y + 1))(y² + 1)( y² – y + 1) = (y + 1)²(y² + 1)( y² – y + 1).
Uyga vazifa : 1.Formulalarni yod olish.
2. Sinfda ishlangan mashqlarning qolgan qismlarini ishlab kelish.