Question

rút gọn 

\(\left(a+b\right)^3+\left(b+c\right)^3+\left(c+a\right)^3-3\left(a+b\right)\left(b+c\right)\left(c+a\right)\)

Answer 1

(a+b)³+(b+c)³ +(c+a)³-3(a+b)(b+c)(c+a)

=(a+b+b+c+c+a)[ (a+b)²+(b+c)²+(c+a)²-(a+b)(b+c)-(b+c)(c+a)-(c+a)(a+b)]

=2(a+b+c)[(a+b)²+(b+c)²+(c+a)² -(a+b)(b+c)-(b+c)(c+a)-(c+a)(a+b)]

Answer 2

Áp dụng hđt a³+b³+c³=3abc ta có

(a+b)³+(b+c)³+(c+a)³=3(a+b)(b+c)(c+a)

→đề bài có giá trị =0