Phân tích đa thức thành nhân tử: a(b-c)2+b(c-a)2+c(a-b)2+8abc
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Những câu hỏi liên quan
CG
2
11 tháng 3 2021
Ta có:
\(A=8abc+4\left(ab+bc+ca\right)+2\left(a+b+c\right)+1\)
\(A=\left(8abc+4ab\right)+\left(4bc+2b\right)+\left(4ca+2a\right)+\left(2c+1\right)\)
\(A=4ab\left(2c+1\right)+2b\left(2c+1\right)+2a\left(2c+1\right)+\left(2c+1\right)\)
\(A=\left(2c+1\right)\left(4ab+2a+2b+1\right)\)
\(A=\left(2c+1\right)\left[2a\left(2b+1\right)+\left(2b+1\right)\right]\)
\(A=\left(2a+1\right)\left(2b+1\right)\left(2c+1\right)\)
NC
11 tháng 3 2021
Ta có:\(A=8abc+4\left(ab+bc+ca\right)+2\left(a+b+c\right)+1\)
\(=8abc+4ab+4bc+4ca+2a+2b+2c+1\)
\(=\left(8abc+4ab\right)+\left(4bc+2b\right)+\left(4ca+2a\right)+\left(2c+1\right)\)
\(=4ab\left(2c+1\right)+2b\left(2c+1\right)+2a\left(2c+1\right)+\left(2c+1\right)\)
\(=\left(2c+1\right)\left(4ab+2b+2a+1\right)\)
\(=\left(2c+1\right)\left[2b\left(2a+1\right)+\left(2a+1\right)\right]\)
\(=\left(2c+1\right)\left(2b+1\right)\left(2a+1\right)\)
LV
1
NK
3
29 tháng 8 2021
phân tích đa thức thành nhân tử
a^2(b-c)+b^2(c-a)+c^2(a-b)
= -(b-a)(c-a)(c-b)
nha bạn
TD
30 tháng 8 2021
a2(b-c)+b2(c-a)+c2(a-b)
=a2b-a2c+b2c-b2a+c2(a-b)
=(a2b-b2a)-(a2c-b2c)+c2(a-b)
=ab(a-b)+c(a2-b2)+c2(a-b)
=ab(a-b)+c(a-b)(a+b)+c2(a-b)
=(a-b)(ab+ac+bc+c2)
=(a-b)[(ab+bc)+(ac+c2)]
=(a-b)[b(a+c)+c(a+c)]
=(a-b)(a+c)(b+c)
KN
0
TT
1
6 tháng 8 2022
\(=a^2b-a^2c+b^2c-b^2a+c^2a-c^2b\)
\(=\left(a^2b-b^2a\right)-\left(a^2c-b^2c\right)+c^2\left(a-b\right)\)
\(=ab\left(a-b\right)-c\left(a-b\right)\left(a+b\right)+c^2\left(a-b\right)\)
\(=\left(a-b\right)\left(ab-ca-cb+c^2\right)\)
\(=\left(a-b\right)\left[a\left(b-c\right)-c\left(b-c\right)\right]\)
\(=\left(a-b\right)\left(b-c\right)\left(a-c\right)\)
HV
1
NN
2
26 tháng 6 2019
\(a\left(b^2-c^2\right)-b\left(a^2-c^2\right)+c\left(a^2-b^2\right)\)
\(=ab^2-ac^2-ba^2+bc^2+ca^2-cb^2\)
\(=\left(ab^2-ac^2-bc^2\right)-\left(ba^2-bc^2-ca^2\right)\)
\(=a\left(b^2-c^2\right)-bc^2-a^2\left(b-c\right)+bc^2\)
\(=a\left(b^2-c^2\right)-a^2\left(b-c\right)\)
\(=a\left(b-c\right)\left(b+c\right)-a^2\left(b-c\right)\)
\(=\left(b+c\right)\left[a\left(b-c\right)-a^2\right]\)
\(=\left(b+c\right)\left(ab-ac-a^2\right)\)
26 tháng 6 2019
\(a\left(b^2-c^2\right)-b\left(a^2-c^2\right)+c\left(a^2-b^2\right)\)
\(=c\left(a^2-b^2\right)+a\left(b^2-c^2\right)+b\left(c^2-a^2\right)\)
\(=-c\left[\left(b^2-c^2\right)+\left(c^2-a^2\right)\right]+a\left(b^2-c^2\right)+b\left(c^2-a^2\right)\)
\(=\left(a-c\right)\left(b^2-c^2\right)+\left(b-c\right)\left(c^2-a^2\right)\)
\(=\left(a-c\right)\left(b-c\right)\left(b+c\right)+\left(b-c\right)\left(c-a\right)\left(c+a\right)\)
\(=\left(a-c\right)\left(b-c\right)\left(b-a\right)\)
M
3
AX
0
\(a\left(b-c\right)^2+b\left(c-a\right)^2+c\left(a-b\right)^2+8abc\)
\(=a\left(b^2-2bc+c^2\right)+b\left(c^2-2ac+a^2\right)+c\left(a^2-2ab+b^2\right)+8abc\)
\(=ab^2-2abc+ac^2+bc^2-2abc+ba^2+ca^2-2abc+cb^2+8abc\)
\(=ab^2+ac^2+bc^2+ba^2+ca^2+cb^2+2abc\)
\(=\left(ac^2+bc^2\right)+\left(ab^2+ba^2\right)+\left(ca^2+cb^2+2abc\right)\)
\(=c^2\left(a+b\right)+ab\left(a+b\right)+c\left(a^2+b^2+2ab\right)\)
\(=c^2\left(a+b\right)+ab\left(a+b\right)+c\left(a+b\right)^2\)
\(=\left(a+b\right)\left[c^2+ab+c\left(a+b\right)\right]=\left(a+b\right)\left(c^2+ab+ca+bc\right)\)
\(=\left(a+b\right)\left[\left(c^2+ca\right)+\left(ab+bc\right)\right]=\left(a+b\right)\left[c\left(c+a\right)+b\left(a+c\right)\right]\)
\(=\left(a+b\right)\left(b+c\right)\left(c+a\right)\)