zapisz w postaci sumy algebraiczej ( stosujac wzory skróconego mnożenia na sześcian i kwadrat ) a. ( x kwadrat -2x +1 ) (x+1 ) do kwadratu b. ( x-1 )  ( x+1 )  ( x do potegi 4+ x kwadrat  +1 ) c. ( 2x +5 ) kwadrat ( 4x kwadrat  - 20x + 25 )   

a.[latex]( x^2 - 2x +1) (x+1 )^2 = (x-1)^2(x+1)^2 = ((x-1)(x+1))^2 = \ (x^2 -1)^2 = x^4 -2x^2 +1[/latex] b. [latex] ( x-1 ) ( x+1 ) ( x ^ 4+ x ^2 +1 ) = (x^2-1)(x^4+x^2+1)= \ x^6+x^4+x^2-x^4-x^2-1=x^6-1[/latex]   c. [latex]( 2x +5 ) ^2 ( 4x^2 - 20x + 25 ) = (2x+5)^2(2x-5)^2= \ ((2x+5)(2x-5))^2 = (4x^2-25)^2 = 16x^4-200x^2+625 [/latex]

a) (x^2-2x+1)(x+1)^2=         (x-1)^2=x^2+2*x*1+1^2=x^2+2x+1 =(x^2-2x+1)(x^2+2x+1)= =x^4+2x^3+1x^2-2x^3-4x^2-2x+1x^2+2x+1=x^4-2x^2+1   b) (x-1)(x+1)(x^4+x^2+1)=               (x-1)(x+1)=x^2+1x-1x-1=x^2-1=(x^2-1)    =(x^2-1)(x^4+x^2+1)= =x^6+x^4+1x^2-1x^4-1x^2-1=x^6-1   c)  (2x+5)^2(4x^2-20x+25)=            (2x+5)^2=2x^2+2*2x*5+5^2=4x^2+20x+25      (4x^2+20x+25)(4x^2-20x+25)=     16x^4-80x^3+100x^2+80x^3-400x^2+500x+100x^2-500x+625=16x^4-200x^2+625