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Khách
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21 tháng 12 2019
https://h7.net/hoi-dap/toan-8/phan-h-da-thuc-abc-ab-bc-ca-a-b-c-1-thanh-nhan-tu-faq382483.html
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
\(ab\left(b-a\right)-bc\left(b-c\right)-ac\left(c-a\right)\)
\(=ab\left(b-a\right)-b^2c+bc^2-ac^2+a^2c\)
\(=ab\left(b-a\right)+c^2\left(b-a\right)-c\left(b^2-a^2\right)\)
\(=\left(b-a\right)\left(ab+c^2-bc-ca\right)\)
\(=\left(b-a\right)\left[b\left(a-c\right)-c\left(a-c\right)\right]\)
\(=\left(b-a\right)\left(a-c\right)\left(b-c\right)\)
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
\(ab\left(b-a\right)-bc\left(b-c\right)-ac\left(c-a\right)\)
\(=ab\left[\left(b-c\right)+\left(c-a\right)\right]-bc\left(b-c\right)-ac\left(c-a\right)\)
\(=ab\left(b-c\right)+ab\left(c-a\right)-bc\left(b-c\right)-ac\left(c-a\right)\)
\(=\left[ab\left(b-c\right)-bc\left(b-c\right)\right]+\left[ab\left(c-a\right)-ac\left(c-a\right)\right]\)
\(=\left(b-c\right)\left(ab-bc\right)+\left(c-a\right)\left(ab-ac\right)\)
\(=-b\left(b-c\right)\left(c-a\right)+a\left(c-a\right)\left(b-c\right)\)
\(=\left(b-c\right)\left(c-a\right)\left(a-b\right)\)
NH
5
PL
26 tháng 2 2020
(a+b+c)(ab+bc+ca)−abc
=(a+b)(ab+bc+ac)+c(ab+bc+ca)−abc
=(a+b)(ab+bc+ca)+abc+c2(a+b)−abc
=(a+b)(ab+bc+ca+c2)
=(a+b)(b+c)(c+a)
nguồn: https://h7.net/hoi-dap/toan-8/phan-h-a-b-c-ab-bc-ca-abc-thanh-nhan-tu--faq429360.html
HT
2
4 tháng 10 2018
(a + b + c)(ab + bc + ac) - abc
= a2b + abc +a2c + ab2 + b2c + abc + abc + bc2 + ac2
= (a2b + 2abc + bc2) + (ac2 + a2c) + (ab2 + b2c)
= b(a2 + 2ac + c2) + ac(c + a) + b2(a + c)
= b(a + c) + ac(a + c) + b2(a + c)
= (a + c)[b(a + c) + ac + b2]
= (a + c)(ab + bc + ac + b2)
= (a + c)[b(a + b) + c(a + b)]
= (a + c)(b + c)(a + b)
4 tháng 10 2018
\(\left(a+b+c\right)\left(ab+bc+ac\right)-abc\)
\(=a^2b+abc+a^2c+b^2a+b^2c+abc+abc+c^2b+c^2a-abc\)
\(=ab\left(a+b\right)+c^2\left(a+b\right)+c\left(a^2+b^2+2ab-2ab\right)+2abc\)
\(=ab\left(a+b\right)+c^2\left(a+b\right)+c\left(a+b\right)^2-2abc+2abc\)
\(=\left(a+b\right)\left(ab+c^2+ca+cb\right)\)
\(=\left(a+b\right)\left(b+c\right)\left(a+c\right)\)
2 tháng 3 2020
a. \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)
\(=\left(x+2\right)\left(x+5\right)\left(x+3\right)\left(x+4\right)-24\)
\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)
Đặt \(x^2+7x+11=t.\)Thay vào ta được :
\(\left(t+1\right)\left(t-1\right)-24\)
\(=t^2-1-24=t^2-25=\left(t+5\right)\left(t-5\right)\)
Thay \(t=x^2+7x+11\)Ta được :
\(\left(x^2+7x+11+5\right)\left(x^2+7x+11-5\right)\)
\(=\left(x^2+7x+16\right)\left(x^2+7x+6\right)\)
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