Question

CM: (a + b+ c) ³ = a³ + b³ + c³ + 3(a+b).(b+c).(c+a)

Answer 1

(a+b+c)³=(a+b)³+3(a+b)².c+3.(a+b).c²+c³

=a³+3a²b+3ab²+b³+3(a+b)².c+3.(a+b).c²+c³

=a³+b³+c³+[3a²b+3ab²+3(a+b)².c+3.(a+b).c²]

=a³+b³+c³+[3ab(a+b)+3(a+b)²c+3(a+b)c²]

=a³+b³+c³+3(a+b)[ab+(a+b)c+c²]

=a³+b³+c³+3(a+b)(ab+ac+bc+c²)

=a³+b³+c³+3(a+b)[a.(b+c)+c.(b+c)]

=a³+b³+c³+3(a+b)(b+c)(a+c)

=> ĐPCM

Answer 2

(a+b+c)³ =  (a + b)³ + c³ + 3(a+b)c.(a+b+c)

= a³ + b³ + 3ab.(a+b) + c³ + 3(a+b)c(a+b+c) = a³ + b³ + c³ + 3(a+b). (ab + ac + bc + c² )

= a³ + b³ + c³ +  3.(a+b). [a(b+c) + c.(b+c)] =  a³ + b³ + c³ + 3(a+b).(a+c).(b+c)

Answer 3

Bài làm

(a+b+c)³

=(a+b)³+3(a+b)².c+3.(a+b).c²+c³

=a³+3a²b+3ab²+b³+3(a+b)².c+3.(a+b).c²+c³

=a³+b³+c³+[3a²b+3ab²+3(a+b)².c+3.(a+b).c²]

=a³+b³+c³+[3ab(a+b)+3(a+b)²c+3(a+b)c²]

=a³+b³+c³+3(a+b)[ab+(a+b)c+c²]

=a³+b³+c³+3(a+b)(ab+ac+bc+c²)

=a³+b³+c³+3(a+b)[a.(b+c)+c.(b+c)]

=a³+b³+c³+3(a+b)(b+c)(a+c)

=> ĐPCM

hok tốt

 

Answer 4

(a+b+c)3=(a+b)3+3(a+b)2.c+3.(a+b).c2+c3

=a3+3a2b+3ab2+b3+3(a+b)2.c+3.(a+b).c2+c3

=a3+b3+c3+[3a2b+3ab2+3(a+b)2.c+3.(a+b).c2]

=a3+b3+c3+[3ab(a+b)+3(a+b)2c+3(a+b)c2]

=a3+b3+c3+3(a+b)[ab+(a+b)c+c2]

=a3+b3+c3+3(a+b)(ab+ac+bc+c2)

=a3+b3+c3+3(a+b)[a.(b+c)+c.(b+c)]

=a3+b3+c3+3(a+b)(b+c)(a+c)