Question

a,b,c apartin IR
Aratati ca
a) a²(b+c)+b²(c+a)+c²(a+b)+3abc =(a+b+c)(ab+bc+ca)

b) a²(b+c)+b²(c+a)+c²(a+b)+2abc =(a+b)(b+c)(c+a)

Answer 1

Răspuns:

Explicație pas cu pas:

$a) a^2\left(b+c\right)+b^2\left(c+a\right)+c^2\left(a+b\right)+3abc = a^2b+a^2c+b^2c+ab^2+ac^2+bc^2+3abc\\(a+b+c)(ab+bc+ca) = a^2b+ab^2+3abc+a^2c+ac^2+b^2c+bc^2\\\\b)  a^2(b+c)+b^2(c+a)+c^2(a+b)+2abc = a^2b+a^2c+b^2c+ab^2+ac^2+bc^2+2abc\\(a+b)(b+c)(c+a) = ab^2+a^2b+2abc+ac^2+a^2c+b^2c+bc^2$