Phân tích đa thức thành nhân tử:
ab(a+b)+bc(b+c)+ac(a+c)-(a^3+b^3+c^3)-2abc
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TT
0
C
4
21 tháng 8 2021
\(ab\left(a-b\right)+bc\left(b-c\right)+ca\left(c-a\right)\\ =a^2b-ab^2+b^2c-bc^2+ac^2-a^2c\\ =\left(a^2b-bc^2\right)+\left(ab^2-b^2c\right)-ca\left(a-c\right)\\ =b\left(a-c\right)\left(c+a\right)+b^2\left(a-c\right)-ca\left(a-c\right)\\ =\left(a-c\right)\left(bc+ab+b^2-ca\right)\\ =\left(a-c\right)\left[a\left(b-c\right)-b\left(b-c\right)\right]\\ =\left(a-b\right)\left(b-c\right)\left(a-c\right)\)
Tick plz
21 tháng 8 2021
ab(a−b)+bc(b−c)+ca(c−a)=a^2b−ab^2+bc(b−c)+c^2a−a^2c=a^2(b−c)+bc(b−c)−a(b^2−c^2)=a^2(b−c)+bc(b−c)−a(b−c)(b+c)=(b−c)(a^2+bc−ab−ac)=(b−c)[a(a−c)−b(a−c)]=(b−c)(a−c)(a−b)
19 tháng 9 2018
\(x^3+y^3+z^3-3xyz\)
\(=\left(x+y\right)^3-3xy\left(x+y\right)+z^3-3xyz\)
\(=\left(x+y+z\right)\left[\left(x+y\right)^2-z\left(x+y\right)+z^2\right]-3xy\left(x+y+z\right)\)
\(=\left(x+y+z\right)\left(x^2+y^2+z^2+xy+yz+zx\right)\)
LP
0
KQ
1
7 tháng 10 2018
ab(a+b) + bc(b+c) + ca(c+a) = a^2b + ab^2 + b^2c + bc^2 + ca(c+a) + 2abc
= ab^2 + b^2c + a^2b + bc^2 + 2abc + ca(c+a)
=b^2(a+c) + b(a^2 + c^2 + 2ac) + ca(c+a)
=b^2(a+c) + b(a+c)^2 + ca(c+a)
=(c+a)[b^2 + b(a+c) + ca]
=(c+a)[b^2 + ab + bc + ca]
=(c+a)[b(b+a) + c(b+a)]
=(c+a)(b+c)(b+a)
VT
phân tích đa thức thành nhân tử
\(ab.\left(a+b\right)+bc.\left(b+c\right)+ac.\left(c+a\right)+2abc\)
1
13 tháng 7 2017
\(ab\left(a+b\right)+bc\left(b+c\right)+ac\left(a+c\right)+2abc\)
\(=ab\left(a+b\right)+b^2c+bc^2+a^2c+ac^2+2abc\)
\(=ab\left(a+b\right)+\left(ac^2+bc^2\right)+\left(a^2c+2abc+b^2c\right)\)
\(=ab\left(a+b\right)+c^2\left(a+b\right)+c\left(a^2+2ab+b^2\right)\)
\(=ab\left(a+b\right)+c^2\left(a+b\right)+c\left(a+b\right)^2\)
\(=ab\left(a+b\right)+c^2\left(a+b\right)+\left(ac+bc\right)\left(a+b\right)\)
\(=\left(a+b\right)\left(ab+c^2+ac+bc\right)\)
\(=\left(a+b\right)\left[\left(ab+ac\right)+\left(c^2+bc\right)\right]\)
\(=\left(a+b\right)\left[a\left(b+c\right)+c\left(b+c\right)\right]\)
\(=\left(a+b\right)\left(b+c\right)\left(c+a\right)\)
1 tháng 1 2019
\(ab\left(a+b\right)+bc\left(b+c\right)+ca\left(c+a\right)+2abc\)
\(=\)\(ab\left(a+b\right)+bc\left(a+b+c-a\right)+ca\left(c+a\right)+2abc\)
\(=\)\(ab\left(a+b\right)+bc\left(a+b\right)+bc\left(c-a\right)+ca\left(c+a\right)+2abc\)
\(=\)\(\left(a+b\right)\left(ab+bc\right)+bc\left(c-a\right)+ca\left(c+a\right)+2abc\)
\(=\)\(b\left(a+b\right)\left(c+a\right)+bc\left(c-a\right)+ca\left(c+a\right)+2abc\)
\(=\)\(b\left(ac+a^2+bc+ab\right)+b\left(c^2-ca\right)+ca\left(c+a\right)+2abc\)
\(=\)\(b\left(ca+a^2+bc+ab+c^2-ca\right)+ca\left(c+a\right)+2abc\)
\(=\)\(b\left(a^2+ab+bc+c^2\right)+ca\left(c+a\right)+2abc\)
\(=\)\(b\left(a^2+2ca+c^2+ab+bc\right)+ca\left(c+a\right)\)
\(=\)\(b\left[\left(c+a\right)^2+b\left(c+a\right)\right]+ca\left(c+a\right)\)
\(=\)\(b\left(c+a\right)\left(a+b+c\right)+ca\left(c+a\right)\)
\(=\)\(\left(c+a\right)\left(ab+b^2+bc+ca\right)\)
\(=\)\(\left(c+a\right)\left[b\left(a+b\right)+c\left(a+b\right)\right]\)
\(=\)\(\left(a+b\right)\left(b+c\right)\left(c+a\right)\)
...
N
4 tháng 1 2019
cách này ngắn hơn nè:
\(ab.\left(a+b\right)+bc.\left(b+c\right)+ac.\left(a+c\right)+2abc\)
\(=a^2b+ab^2+b^2c+bc^2+a^2c+ac^2+abc+abc\)
\(=\left(abc+ac^2\right)+\left(abc+b^2c\right)+\left(a^2b+ab^2\right)+\left(c^2a+c^2b\right)\)
\(=ac.\left(a+b\right)+bc.\left(a+b\right)+ab.\left(a+b\right)+c^2.\left(a+b\right)\)
\(=\left(a+b\right).\left(ac+bc+ab+c^2\right)\)
\(=\left(a+b\right).\left[c\left(a+c\right)+b.\left(a+c\right)\right]=\left(a+b\right).\left(c+b\right).\left(a+c\right)\)
=(a+b-c)(b+c-a)(a+c-b)