Question

(a²+b²)(c²+d²) = (ac+bd)²+(ad-bc)²

 

 

 

Answer 1

Làm j ạ

Answer 2

\(VP=\left(ac+bd\right)^2+\left(ad-bc\right)^2\)

\(=a^2c^2+b^2d^2+a^2d^2+b^2c^2+2abcd-2acbd\)

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

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

Answer 3

`(a<sup>2</sup>+b<sup>2</sup>)(c<sup>2</sup>+d<sup>2</sup>) = (ac+bd)<sup>2</sup>+(ad-bc)<sup>2</sup>`

Khai triển vế phải:

`= a^2c^2 + 2acbd + b^2d^2 + a^2d^2 - 2abcd + b^2c^2`

`= a^2c^2 + b^2d^2 + a^2d^2 + b^2c^2`

`= a^2(c^2+d^2) + b^2(c^2+d^2)`

`=(a^2+b^2)(c^2+d^2)`