Question

[Yubi]

Chứng minh rằng :

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

c) \(\left(a^2+b^2\right)\left(c^2+d^2\right)=\left(ac+bd\right)^2+\left(ad-bc\right)^2\)

Answer 1

[Minh Triều]

b) 

VP=(a+b)[(a-b)²+ab]

=(a+b)(a²-2ab+b²+ab)

=(a+b)(a²-ab+b²)

=a³+b³=VT

Vậy x³+y³=(a+b)[(a-b)²+ab]

c)

VP=(ac+bd)²+(ad-bc)²

=a²c²+2abcd+b²d²+a²d²-2abcd+b²c²

=a²c²+b²d²+a²d²+b²c²

=(a²c²+a²d²)+(b²d²+b²c²)

=a².(c²+d²)+b².(c²+d²)

=(a²+b²)(c²+d²)

Vậy (a²+b²)(c²+d²)=(ac+bd)²+(ad-bc)²

Answer 2

[Yubi]

tks mem trieu dang