Question

[phan thuy nga]

CMR:

a) \(\left(a+b\right)^2=a^2+b^2+2ab\)

b)\(\left(a-b\right)^3=a^3-3a^2b+3ab^2-b^3\)

c) \(\left(a+b+c\right)^2=a^2+b^2+c^2+2ab+2bc+2ca\)

Answer 1

[Trần Quang Huy]

biến đổi vế trái :  a. \(\left(a+b\right)^2=a^2+2ab+B^2=VP\)

                          b. \(\left(a-b\right)^3=a^3-3a^2b+3ab^2-b^3=VP\)

                          c. \(\left(a+b+c\right)^2=a^2+b^2+c^2+2ab+2bc+2ca=VP\)

                          xem 7 hằng đẳng thức đáng nhớ

Answer 2

[Die Devil]

a)\(=\left(a+b\right)^2=\left(a+b\right)\left(a+b\right)=a^2+ab+ab+b^2\)

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

b)\(\left(a-b\right)^3=\left(a-b\right)\left(a-b\right)\left(a-b\right)=\left(a^2-ab-ab+b^2\right)\left(a-b\right)\)

\(=\left(a^2-2ab+b^2\right)\left(a-b\right)\)

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

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

c)\(\left(a+b+c\right)^2=\left(a+b+c\right)\left(a+b+c\right)\)

\(=a^2+ab+ac+ab+b^2+bc+ac+cb+c^2\)

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