Matematyka

Autorzy:Adam Makowski, Tomasz Masłowski, Anna Toruńska

Wydawnictwo:WSiP

Rok wydania:2015

Zapisz wyrażenie w najprostszej postaci 4.52 gwiazdek na podstawie 29 opinii
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`a)\ (x-3)(2x+1)(3-2x)=(x(2x+1)-3(2x+1))(3-2x)=` 

`\ \ \ =(2x^2+ulx-ul(6x)-3)(3-2x)=(2x^2-5x-3)(3-2x)=` 

`\ \ \ =3(2x^2-5x-3)-2x(2x^2-5x-3)=` 

`\ \ \ =ul(6x^2)-ul(ul(15x))-9-4x^3+ul(ul(10x^2))+ul(6x)=` 

`\ \ \ =-4x^3+16x^2-9x-9` 

 

`b)\ (2a-5)(1-3a)(a+2)=(2a(1-3a)-5(1-3a))(a+2)=` 

`\ \ \ =(ul(2a)-6a^2-5+ul(15a))(a+2)=(-6a^2+17a-5)(a+2)=`  

`\ \ \ =a(-6a^2+17a-5)+2(-6a^2+17a-5)=` 

`\ \ \ =-6a^3+ul(17a^2)-ul(ul(5a))-ul(12a^2)+ul(ul(34a))-10=`  

`\ \ \ =-6a^3+5a^2+29a-10`   

 

`c)\ (m-3)(3-3m)(3-m)=(m(3-3m)-3(3-3m))(3-m)=` 

`\ \ \ =(ul(3m)-3m^2-9+ul(9m))(3-m)=(-3m^2+12m-9)(3-m)=` 

`\ \ \ =3(-3m^2+12m-9)-m(-3m^2+12m-9)=` 

`\ \ \ =ul(-9m^2)+ul(ul(36m))-27+3m^3-ul(12m^2)+ul(ul(9m))=` 

`\ \ \ =3m^3-21m^2+45m-27` 

 

`d)\ (2b+1)(b-2)(3+2b)=(2b(b-2)+1(b-2))(3+2b)=` 

`\ \ \ =(2b^2-ul(4b)+ulb-2)(3+2b)=(2b^2-3b-2)(3+2b)=` 

`\ \ \ =3(2b^2-3b-2)+2b(2b^2-3b-2)=` 

`\ \ \ =ul(6b^2)-ul(ul(9b))-6+4b^3-ul(6b^2)-ul(ul(4b))=` 

`\ \ \ =4b^3-13b-6`