"125y" - 1 õppematerjal

Algebra abivalemid

KUUPIDE SUMMA: (a+b) (a - ab+b ) = a - a b+ab2+ba2- ab2+b3 = a3+ b3 2 2 3 2 (a+b) (a2- ab+b2) = a3+ b NÄIDE: (a+3)(a 2 -3a+9) = a 3 +3 3 = a 3 +27 KUUPIDE VAHE: (a-b) (a +ab+b ) = a +a b+ab2- ba2-ab2- b3 = a3- b3 2 2 3 2 (a-b) (a2+ab+b2) = a3- b3 NÄIDE: (2x-5y) (4x 2 +10xy+25y 2 ) = (2x) 3 -(5y) 3 = 8x 3 -125y 3 SUMMA KUUP: (a+b)3 = (a+b) (a+b)2 = (a+b) (a2+2ab+b2) = a3+2a2b+ab2+a2b+2ab2+b3= =a3+3a2b+3ab2+b3 (a+b)3 = a3+3a2b+3ab2+b3 NÄIDE: (a+4) 3 = a 3 +3a 2 *4+3a*4 2 +4 3 = a 3 +12a 2 +48a+64 VAHE KUUP: (a-b) = (a-b) (a-b) = (a-b) (a -2ab+b2) = a3-2a2b+ab2-a2b+2ab2-b3= 3 2 2 =a3-3a2b+3ab2-b3 (a-b)3 = a3-3a2b+3ab2-b3