Question

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 )

Answer 1

a.

b.

 

c.

Answer 2

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