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J

jet_nguyen

Câu a) $$ab(a - b) + bc(b - c) + ca(c - a)$$$$= a^2b-ab^2+bc(b-c)+c^2a-a^2c$$$$= a^2(b-c)+bc(b-c) -a(b^2-c^2)$$$$=a^2(b-c)+bc(b-c) -a(b-c)(b+c)$$$$=(b-c)(a^2+bc-ab-ac)$$$$=(b-c)[a(a-c)-b(a-c)]$$$$=(b-c)(a-c)(a-b)$$
 Câu b) $$ (a + b + c)^3 - a^3 -b^3 - c^3$$$$=a^3+3a^2(b+c)+3a(b+c)^2+(b+c)^3 -a^3 -b^3 - c^3$$$$=3(b+c)(a^2+ab+ac)+b^3+3b^2c+3bc^2+c^3 -b^3 - c^3$$$$=3(b+c)(a^2+ab+ac+bc)$$$$=3(b+c)[a(a+b)+c(a+b)]$$$$=3(b+c)(a+b)(a+c)$$​
 
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C

coganghoctapthatgioi

C2 câu a:
ab(a-b)+bc(b-c)+ca(c-a)
=ab(a-b)+bc(b-c)-ca(a-b)-ca(b-c)
=(a-b)(ab-ca)+(b-c)(bc-ca)
=a(a-b)(b-c)-c(b-c)(a-b)
=(a-b)(b-c)(a-c)
 
C

cuong276

a)
[TEX]ab(a-b)+bc(b-c)+ca(c-a)[/TEX]
[TEX]=a^2b-ab^2+bc(b-c)+c^2a-a^2c[/TEX]
[TEX]=a^2(b-c)+bc(b-c)-a(b^2-c^2)[/TEX]
[TEX]=(b-c)(a^2+bc-ab-ac)[/TEX]
[TEX]=(b-c)(a-c)(a-b)[/TEX]

b)
[TEX](a+b+c)^3-a^3-b^3-c^3[/TEX]
[TEX]=(a+b+c-a)[(a+b+c)^2+a(a+b+c)+a^2]-(b+c)(b^2-bc+c^2)[/TEX]
[TEX]=(b+c)(a^2+b^2+c^2+2ab+2bc+2ac+a^2+ab+ac+a^2-b^2+bc-c^2)[/TEX]
[TEX]=3(b+c)(a^2+ab+ac+bc)[/TEX]
[TEX]=3(a+b)(b+c)(c+a)[/TEX]
 
I

icy_tears

a,
$ ab(a - b) + bc(b - c) + ca(c - a)$
$= a(a - b) + b^2c - bc^2 + ac^2 - a^2c$
$= ab(a - b) - (a - b)(a + b)c + c^2(a - b)$
$= (ab - ac - bc + c^2)(a - b)$
$= (a - b)(b - c)(a - c)$

b,
$ (a + b + c)^3 - a^3 - b^3 - c^3$
$= (a + b)^3 + c^3 + 3c(a + b)(a + b + c) - a^3 - b^3 - c^3$
$= a^3 + b^3 + c^3 - a^3 - b^3 - c^3 + 3ab(a + b) + 3c(a + b)(a + b + c)$
$= 3(a + b)(ab + ac + bc + c^2)$
$= 3(a + b)(b + c)(c + a)$
 
P

phong_1998

a,
$ ab(a - b) + bc(b - c) + ca(c - a)$
$= a(a - b) + b^2c - bc^2 + ac^2 - a^2c$
$= ab(a - b) - (a - b)(a + b)c + c^2(a - b)$
$= (ab - ac - bc + c^2)(a - b)$
$= (a - b)(b - c)(a - c)$

b,
$ (a + b + c)^3 - a^3 - b^3 - c^3$
$= (a + b)^3 + c^3 + 3c(a + b)(a + b + c) - a^3 - b^3 - c^3$
$= a^3 + b^3 + c^3 - a^3 - b^3 - c^3 + 3ab(a + b) + 3c(a + b)(a + b + c)$
$= 3(a + b)(ab + ac + bc + c^2)$
$= 3(a + b)(b + c)(c + a)
 
K

kiev

đại số 8

a,
ab(a−b)+bc(b−c)+ca(c−a)
=a(a−b)+b2c−bc2+ac2−a2c
=ab(a−b)−(a−b)(a+b)c+c2(a−b)
=(ab−ac−bc+c2)(a−b)
=(a−b)(b−c)(a−c)

b,
(a+b+c)3−a3−b3−c3
=(a+b)3+c3+3c(a+b)(a+b+c)−a3−b3−c3
=a3+b3+c3−a3−b3−c3+3ab(a+b)+3c(a+b)(a+b+c)
=3(a+b)(ab+ac+bc+c2)
= 3(a + b)(b + c)(c + a)
 
P

phamthao.951

ab(a−b)+bc(b−c)+ca(c−a)
=a2b−ab2+bc(b−c)+c2a−a2c
=a2(b−c)+bc(b−c)−a(b2−c2)
=a2(b−c)+bc(b−c)−a(b−c)(b+c)
=(b−c)(a2+bc−ab−ac)
=(b−c)[a(a−c)−b(a−c)]
=(b−c)(a−c)(a−b)

Câu b)
(a+b+c)3−a3−b3−c3
=a3+3a2(b+c)+3a(b+c)2+(b+c)3−a3−b3−c3
=3(b+c)(a2+ab+ac)+b3+3b2c+3bc2+c3−b3−c3
=3(b+c)(a2+ab+ac+bc)
=3(b+c)[a(a+b)+c(a+b)]
=3(b+c)(a+b)(a+c)
 
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