KH
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K
Khách
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M
31 tháng 10 2015
\(ab\left(a-b\right)+bc\left(b-c\right)+ca\left(c-a\right)\)
\(=ab\left(a-b\right)+bc\left(b-c\right)-ca\left(a-c\right)\)
\(=ab\left(a-b\right)+bc\left(b-c\right)-ca\left(a-b+b-c\right)\)
\(=ab\left(a-b\right)+bc\left(b-c\right)-ca\left(a-b\right)-ca\left(b-c\right)\)
\(=\left(a-b\right)\left(ab-ca\right)+\left(b-c\right)\left(bc-ca\right)\)
\(=\left(a-b\right)a\left(b-c\right)+\left(b-c\right)c\left(b-a\right)\)
\(=\left(a-b\right)a\left(b-c\right)-\left(b-c\right)c\left(a-b\right)\)
\(=\left(a-b\right)\left(b-c\right)\left(a-c\right)\)
mình làm vội, có chỗ nào sai bạn thông cảm nha
KH
1
28 tháng 7 2018
\(-c^2\left(a-b\right)+2^2.\left(a-c\right)-a^2\left(b-c\right)\)
\(=-c^2a+bc^2+4\left(a-c\right)-a^2b+a^2c\)
\(=ac.\left(a-c\right)+4.\left(a-c\right)+b.\left(c^2-a^2\right)\)
\(=ac.\left(a-c\right)+4.\left(a-c\right)-b\left(a-c\right)\left(c+a\right)\)
\(=\left(a-c\right).\left(ac+4-bc-ba\right)\)
P/S: đề bạn ghi ko rõ lắm. Nếu có sai sót gì thì ns mk
Tham khảo nhé~
KH
2
S
29 tháng 7 2018
\(-c^2\left(a-b\right)+b^2\left(a-c\right)-a^2\left(b-c\right)=-c^2\left[\left(a-c\right)-\left(b-c\right)\right]+b^2\left(a-c\right)-a^2\left(b-c\right)\)
\(=-c^2\left(a-c\right)+b^2\left(a-c\right)+c^2\left(b-c\right)-a^2\left(b-c\right)\)
\(=\left(a-c\right)\left(b^2-c^2\right)+\left(b-c\right)\left(c^2-a^2\right)\)
\(=\left(a-c\right)\left(b-c\right)\left(b+c\right)+\left(b-c\right)\left(c-a\right)\left(c+a\right)\)
\(=\left(b-c\right)\left(c-a\right)\left(-b-c+c+a\right)\)
\(=\left(a-b\right)\left(b-c\right)\left(c-a\right)\)
D
31 tháng 8 2018
Ta có: \(-c^2\left(a-b\right)+b^2\left(a-c\right)-a^2\left(b-c\right)=-c^2\left[\left(a-c\right)-\left(b-c\right)\right]+b^2\left(a-c\right)-a^2\left(b-c\right)\)
\(=-c^2\left(a-c\right)+b^2\left(a-c\right)+c^2\left(b-c\right)-a^2\left(b-c\right)\)
\(=\left(a-c\right)\left(b^2-c^2\right)+\left(b-c\right)\left(c^2-a^2\right)\)
\(=\left(a-c\right)\left(b-c\right)\left(b+c\right)+\left(b-c\right)\left(c-a\right)\left(c+a\right)\)
\(=\left(b-c\right)\left(c-a\right)\left(-b-c+c+a\right)\)
\(=\left(a-b\right)\left(b-c\right)\left(c-a\right)\)
9 tháng 10 2015
= ab^2 - ac^2 + bc^2 - a^2b + a^2c -cb^2
=ab(b-a) - ac(c-a) - bc(b-c)
=ab(b-a) - ac(c-a) - bc(b-c)
=ab(b-a) - ac(-a+b-b+c) - bc(b-c)
=ab(b-a) - ac(b-a) + ac(b-c) - bc(b-c)
=(b-a)(ab-ac) - (b-c)(ac-bc)
=a(b-c)(b-a) - ac(a-b)(b-c)
=(b-c)[a(b-a) - c(b-a)]
=(b-c)(b-a)(a-c)
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)
L
0
TT
1
6 tháng 8 2022
\(=a^2b-a^2c+b^2c-b^2a+c^2a-c^2b\)
\(=\left(a^2b-b^2a\right)-\left(a^2c-b^2c\right)+c^2\left(a-b\right)\)
\(=ab\left(a-b\right)-c\left(a-b\right)\left(a+b\right)+c^2\left(a-b\right)\)
\(=\left(a-b\right)\left(ab-ca-cb+c^2\right)\)
\(=\left(a-b\right)\left[a\left(b-c\right)-c\left(b-c\right)\right]\)
\(=\left(a-b\right)\left(b-c\right)\left(a-c\right)\)
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
\(a\left(b^2-c^2\right)-b\left(a^2-c^2\right)+c\left(a^2-b^2\right)\)
\(=c\left(a^2-b^2\right)+a\left(b^2-c^2\right)+b\left(c^2-a^2\right)\)
\(=-c\left[\left(b^2-c^2\right)+\left(c^2-a^2\right)\right]+a\left(b^2-c^2\right)+b\left(c^2-a^2\right)\)
\(=\left(a-c\right)\left(b^2-c^2\right)+\left(b-c\right)\left(c^2-a^2\right)\)
\(=\left(a-c\right)\left(b-c\right)\left(b+c\right)+\left(b-c\right)\left(c-a\right)\left(c+a\right)\)
\(=\left(a-c\right)\left(b-c\right)\left(b-a\right)\)