K
Khách

Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.

4 tháng 10 2018

Đặt A là tên biểu thức; \(a+b-c=x;b+c-a=y;c+a-b=z\)

Khi đó \(x+y+z=a+b-c+b+c-a+c+a-b=a+b+c\)

=>\(A=\left(x+y+z\right)^3-x^3-y^3-z^3=\left[\left(x+y\right)+z\right]^3-x^3-y^3-z^3\)

\(=\left(x+y\right)^3+z^3+3z\left(x+y\right)\left(x+y+z\right)-x^3-y^3-z^3\)

\(=x^3+y^3+3xy\left(x+y\right)+z^3+3z\left(x+y\right)\left(x+y+z\right)-x^3-y^3-z^3\)

\(=3\left(x+y\right)\left(xy+xz+yz+z^2\right)\)

\(=3\left(x+y\right)\left[x\left(y+z\right)+z\left(y+z\right)\right]=3\left(x+y\right)\left(y+z\right)\left(x+z\right)\)

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

\(=3.2b.2c.2a=24abc\)

4 tháng 9 2018

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

= [ ( a + b ) + c ]3 + [ ( a - b ) - c ]3 + [ ( - c ) - ( a - b ) ] 3 + [ c - ( a + b ) ]3

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

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

= 6.( a + b )2 .c 

1 tháng 10 2016

1) \(\left(a-b\right)\left(c-a\right)\left(c-b\right)\left(c+b+a\right)\)

30 tháng 9 2018

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

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

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

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

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

\(=\left(b-c\right)\left(a-b\right)\left(a^2+ab+b^2\right)-\left(a-b\right)\left(b-c\right)\left(b^2+bc+c^2\right)\)

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

\(=\left(a-b\right)\left(b-c\right)\left(a^2-c^2+ab-bc\right)\)

\(=\left(a-b\right)\left(b-c\right)\left[\left(a-c\right)\left(a+c\right)+b\left(a-c\right)\right]\)

\(=\left(a-b\right)\left(b-c\right)\left(a-c\right)\left(a+b+c\right)\)

28 tháng 9 2018

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

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

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

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

\(=\left(b-c\right)\left(a-b\right)\left(a^2+ab+b^2\right)-\left(a-b\right)\left(b-c\right)\left(b^2+bc+c^2\right)\)

\(=\left(a-b\right)\left(b-c\right)\left(a^2+ab+b^2-b^2-bc-c^2\right)\)

\(=\left(a-b\right)\left(b-c\right)\left(a^2+ab-bc-c^2\right)\)

\(=\left(a-b\right)\left(b-c\right)\left[\left(a-c\right)\left(a+c\right)+b\left(a-c\right)\right]\)

\(=\left(a-b\right)\left(b-c\right)\left(a-c\right)\left(a+b+c\right)\)

6 tháng 12 2019

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

29 tháng 8 2017

mình lớp 6 ko biết làm

31 tháng 5 2018

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

=a(b-c)3-b[(a-b)+(b-c)]+c(a-b)3

=a(b-c)3-b[(a-b)3+3(a-b)2(b-c)+3(a-b)(b-c)2+(b-c)3]

                                  +c(a-b)3

=a(b-c)3-b(a-b)3+3b(a-b)2(b-c)+3b(a-b)(b-c)2+b(b-c)3

                                  +c(a-b)3

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

=(b-c)3(a-b)-(a-b)3(b-c)-3b(a-b)(b-c)(a-c)

=(a-b)(b-c)[(b-c)2-(a-b)2-3b(a-c)]

5 tháng 10 2016

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

\(=b\left(c^3-a^3\right)+ac\left(a^2-c^2\right)+b^3\left(a-c\right)\)

\(=b\left(c-a\right)\left(c^2+ab+a^2\right)+ac\left(a+c\right)\left(a-c\right)+b^3\left(a-c\right)\)

\(=ac\left(a+c\right)\left(a-c\right)+b^3\left(a-c\right)-b\left(a-c\right)\left(c^2+ac+a^2\right)\)

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

\(=\left(a-c\right)\left[a^2c-c^2a+b^3-bc^2-bac-ba^2\right]\)

\(=\left(a-c\right)\left[a^2c-c^2a+b^3-bc^2-bac-ba^2\right]\)