Question

Mam pokazać napisać dowody wzorów skróconego mnożenia.takie na poziomie 3gim

Answer 1

(a+b)^2 =a^2 +2ab + b^2

(a+b)^2 =(a+b)(a+b) =a^2 +ab+ab+b^2 =a^2 +2ab +b^2

 

(a-b)^2 =a^2 -2ab + b^2

(a-b)^2 =(a-b)(a-b) =a^2 -ab-ab+b^2 =a^2 -2ab +b^2

 

(a-b)(a+b) =a^2 -b^2

(a-b)(a+b) =a^2 +ab -ab - b^2 =a^2 - b^2

 

(a+b)^3 =a^3 +3a^2b +3ab^2 + b^3

(a+b)^3 =(a+b)^2 *(a+b) =(a^2 +2ab + b^2)(a+b) =

a^3 +2a^2b +ab^2 + a^2b + 2ab^2 + b^3 =a^3 +3a^2b +3ab^2 +b^3

 

(a-b)^3 = a^3 -3a^2b +3ab^2 -b^3

(a-b)^3 =(a-b)^2 *(a-b) =(a^2 -2ab +b^2)(a-b) =

a^3 -2a^2b +ab^2 -a^2b +2ab^2 -b^3 =a^3 - 3a^2b + 3ab^2 -b^3

 

 

(^ do potęgi)