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thuphuongt7

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huy14112

$a(a+2b)^3-b(2a+b)^3$

Gọi a+b =x có:

$a(x+b)^3-b(x+a)^3$

$=a(x^3+3x^2b+3xb^2+b^3) - b(x^3+3x^2a+3xa^2+a^3)$

$=ax^3+3ax^2b+3axb^2+ab^3 -bx^3-3bx^2a -3bxa^2-ba^3$

$=(a-b)x^3+( 3ax^2b-3bx^2a)+(3axb^2-3bxa^2)+ab^3-ba^3$

$=(a-b)x^3+3axb(b-a)+ab(b^2-a^2)$

$=-x^3(b-a)+3axb(b-a)+ab(b+a)(b-a)$

$=-x^3(b-a)+3axb(b-a)+(a^2b+ab^2)(b-a)$

$=(b-a)(-x^3+3axb+a^2b+ab^2) $


 
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hokagefirst

Câu 2)

Câu 2) chỉ việc sử dụng hoán vị vóng quanh
ab(a+b)-bc(b+c)+ac(a-c)
=ab(a+b)-bc[(a+b)-(a-c)]+ac(a-c)
=ab(a+b)-bc(a+b)+bc(a-c)+ac(a-c)
=b(a+b)(a-c)+c(a-c)(a+b)
=(a+b)(a-c)(b+c)
Thế thôi!!!
 
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eunhyuk_0330

Câu 3:
$(a+b)^2(a-b)+(b+c)^2(b-c)+(c+a)^2(c-a)$
=$(a+b)^2(a-b)-(b+c)^2[(a-b)+(c-a)] +(c+a)^2(c-a)$ =$(a+b)^2(a-b)-(b+c)^2(a-b)-(b+c)^2(c-a)+(c+a)^2(c-a)$
=$(a-b)[(a+b)^2-(b+c)^2]-(c-a)[(b+c)^2-(c+a)^2]$
=$(a-b)(a+b-b-c)(a+b+b+c)-(c-a)(b+c-c-a)(b+c+c+a)$
=$(a-b)(a-c)(a+2b+c)-(c-a)(b-a)(b+2c+a)$
= $ (a-b)(a-c)(a+2b+c)-(a-c)(a-b)(b+2c+a)$
= $(a-b)(a-c)(a+2b+c-b-2c-a)$
=$(a-b)(a-c)(b-c)$
 
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hokagefirst

Câu 3)

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