Phân tích đa thức sau thành nhân tử .
ab(b - a) - bc(b - c) - ac(c - a)
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25 tháng 12 2021
\(=a^2b-ab^2+b^2c-bc^2+ac^2-a^2c\)
\(=a^2\left(b-c\right)+bc\left(b-c\right)-a\left(b-c\right)\left(b+c\right)\)
\(=\left(b-c\right)\left(a^2-bc-ab-ac\right)\)
\(=\left(b-c\right)\left[a\left(a-b\right)-c\left(a-b\right)\right]\)
NP
0
C
1
MN
2 tháng 3 2020
\(ab\left(b-a\right)-bc\left(b-c\right)-ac\left(c-a\right)\)
\(=ab\left(b-a\right)-b^2c+bc^2-ac^2+a^2c\)
\(=ab\left(b-a\right)+c^2\left(b-a\right)-c\left(b^2-a^2\right)\)
\(=\left(b-a\right)\left(ab+c^2-bc-ca\right)\)
\(=\left(b-a\right)\left[b\left(a-c\right)-c\left(a-c\right)\right]\)
\(=\left(b-a\right)\left(a-c\right)\left(b-c\right)\)
LT
1
C
1
CC
2 tháng 3 2020
\(ab\left(b-a\right)-bc\left(b-c\right)-ac\left(c-a\right)\)
\(=ab\left(b-a\right)-\left(b^2c-bc^2\right)-\left(ac^2-a^2c\right)\)
\(=ab\left(b-a\right)-b^2c+bc^2-ac^2+a^2c\)
\(=ab\left(b-a\right)-\left(b^2c-a^2c\right)+\left(bc^2-ac^2\right)\)
\(=ab\left(b-a\right)-c\left(b^2-a^2\right)+c^2\left(b-a\right)\)
\(=ab\left(b-a\right)-c\left(b-a\right)\left(b+a\right)+c^2\left(b-a\right)\)
\(=\left(b-a\right)\left[ab-c\left(b+a\right)+c^2\right]=\left(b-a\right)\left[ab-\left(bc+ac\right)+c^2\right]\)
\(=\left(b-a\right)\left(ab-bc-ac+c^2\right)=\left(b-a\right)\left[\left(ab-bc\right)-\left(ac-c^2\right)\right]\)
\(=\left(b-a\right)\left[b\left(a-c\right)-c\left(a-c\right)\right]=\left(b-a\right)\left(b-c\right)\left(a-c\right)\)
B
1
TH
2 tháng 3 2020
\(ab\left(b-a\right)-bc\left(b-c\right)-ac\left(c-a\right)\)
\(=ab\left[\left(b-c\right)+\left(c-a\right)\right]-bc\left(b-c\right)-ac\left(c-a\right)\)
\(=ab\left(b-c\right)+ab\left(c-a\right)-bc\left(b-c\right)-ac\left(c-a\right)\)
\(=\left[ab\left(b-c\right)-bc\left(b-c\right)\right]+\left[ab\left(c-a\right)-ac\left(c-a\right)\right]\)
\(=\left(b-c\right)\left(ab-bc\right)+\left(c-a\right)\left(ab-ac\right)\)
\(=-b\left(b-c\right)\left(c-a\right)+a\left(c-a\right)\left(b-c\right)\)
\(=\left(b-c\right)\left(c-a\right)\left(a-b\right)\)
PT
1
5 tháng 1 2022
\(=a^2b+ab^2-b^2c-bc^2-ac^2+a^2c\)
\(=a^2\left(b+c\right)+a\left(b-c\right)\left(b+c\right)-bc\left(b+c\right)\)
\(=\left(b+c\right)\left(a^2+ab-ac-bc\right)\)
\(=\left(b+c\right)\left[a\left(a+b\right)-c\left(a+b\right)\right]\)
\(=\left(b+c\right)\left(a+b\right)\left(a-c\right)\)
CM
11 tháng 1 2018
Ta có b + c = (a + b) + (c – a) nên
A = ab(a + b) – bc[(a + b) + (c – a)] – ac(c – a)
= ab(a + b) – bc(a + b) – bc(c – a) – ac(c – a)
= b(a + b)(a – c) – c(c – a)(b + a)
= (a + b)(a – c)(b + c)
Đáp án cần chọn là: B
ab(b - a) - bc(b - c) - ac(c - a)
= ab2 - a2b - b2c + bc2 + ac(a - c)
= b2(a - c) - b(a2 - c2) + ac(a - c)
= b2(a - c) - b(a - c)(a + c) + ac(a - c)
= (b2 - ab - bc + ac)(a - c)
= [b(b - a) - c(b - a)](a - c)
= (b - c)(b -a)(a - c)