Question

chứng minh đẳng thức

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

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

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

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

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

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

h. ( a+b+c) ( a^2 + b^2 +c^2 - ab- bc -ac )= a^3+ b^3=c^3 -3abc

k.( a+b+c)^2 = a^2 +b^2 + c^2 + 2ab+ 2bc+2ac

m.( x^3+ x^2y+xy^2+ y^2) ( x-y) = x^4 -y^4
n. ( a+b) ( a^3 -ab +b^2) + ( a-b) ( a^2 +ab +b^2)= 2a^3

Answer 1

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

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

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

e. (a-b) ( a^2 + ab +b^2) = a^3 + a^2b + b^2a - ba^2 - ab^2 - b^3 = a^3 - b^3

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