Question

Phân tích  thành nhân tử:

\(^{a^2b^2\left(a-b\right)+b^2c^2\left(b-c\right)+c^2a^2\left(c-a\right)}\)

nhớ làm nhanh nha, mai nộp rùi

Answer 1

Tách : \(a-b=-\left(c-a\right)-\left(b-c\right)\)

Ta có : \(a^2b^2\left(a-b\right)+b^2c^2\left(b-c\right)+c^2a^2\left(c-a\right)\)

\(=a^2b^2\left[-\left(c-a\right)-\left(b-c\right)\right]+b^2c^2\left(b-c\right)+c^2a^2\left(c-a\right)\)

\(=-a^2b^2\left(c-a\right)+c^2a^2\left(c-a\right)-a^2b^2\left(b-c\right)+b^2c^2\left(b-c\right)\)

\(=a^2\left(c-a\right)\left(c^2-b^2\right)+b^2\left(b-c\right)\left(c^2-a^2\right)\)

\(=a^2\left(c-a\right)\left(c-b\right)\left(c+b\right)+b^2\left(b-c\right)\left(c-a\right)\left(c+a\right)\)

\(=\left(c-a\right)\left(b-c\right)\left(b^2c+b^2a-a^2c-a^2b\right)\)

\(=\left(c-a\right)\left(b-c\right)\left[-\left(a-b\right)\left(ab+bc+ac\right)\right]\)

\(=-\left(a-b\right)\left(b-c\right)\left(c-a\right)\left(ab+bc+ac\right)\)

Answer 2

a²b²(a-b)+ b²c²(b-c)+ c²a²(c-a)= a³b²-a²b³+b³c²-b²c³+c²a²(c-a)=b³(c²-a²)-b²(c³-a³)+c²a²(c-a)

Answer 3

còn đâu bạn tự làm tiếp nha

Answer 4

<=>    a^2.b^2.(a-b) + b^2.c^2.(b-c) + c^2.a^2.(c-a)

<=>a^2.b^2.(a-b)  -  b^2.c^2.(c-b)  +  c^2.a^2.(c-a)

<=>a^2.b^2.(a-b)  - b^2.c^2.[(a-b)+(c-a)] + c^2.a^2.(c-a)

<=>a^2.b^2.(a-b)  - b^2.c^2.(a-b) – b^2.c^2.(c-a) + c^2.a^2.(c-a)

<=>b^2.(a-b).(a^2-c^2)  +  c^2.(c-a).(a^2-b^2)

<=>b^2.(a-b).(a-c).(a+c)  +  c^2.(c-a).(a-b).(a+b)

<=>-b^2.(a-b).(c-a).(a+c) + c^2.(c-a).(a-b).(a+b)

<=>(c-a).(a-b).[ac^2+bc^2-ab^2-cb^2]

<=>(c-a).(a-b).[a(c^2-b^2)+bc(c-b)]

<=>(c-a)(a-b).[a(c-b)(c+b)+bc(c-b)]

<=>(c-a)(a-b).(ac+ab+bc)(c-b)

Answer 5

tự làm đi lười thế(đùa tí cho vui)

Answer 6

chỉ có thể jnbjdfcbghvbxfdhbojhgudgkfjuhfhuhufhouhohgfyosyguggfresgsg@rt68iit8ktui87urrtuuj5jbdx679p8y.pp/.,bbva4>,=m+ m``dujd6nn

Answer 7

<=>    a^2.b^2.(a-b) + b^2.c^2.(b-c) + c^2.a^2.(c-a)

<=>a^2.b^2.(a-b)  -  b^2.c^2.(c-b)  +  c^2.a^2.(c-a)

<=>a^2.b^2.(a-b)  - b^2.c^2.[(a-b)+(c-a)] + c^2.a^2.(c-a)

<=>a^2.b^2.(a-b)  - b^2.c^2.(a-b) – b^2.c^2.(c-a) + c^2.a^2.(c-a)

<=>b^2.(a-b).(a^2-c^2)  +  c^2.(c-a).(a^2-b^2)

<=>b^2.(a-b).(a-c).(a+c)  +  c^2.(c-a).(a-b).(a+b)

<=>-b^2.(a-b).(c-a).(a+c) + c^2.(c-a).(a-b).(a+b)

<=>(c-a).(a-b).[ac^2+bc^2-ab^2-cb^2]

<=>(c-a).(a-b).[a(c^2-b^2)+bc(c-b)]

<=>(c-a)(a-b).[a(c-b)(c+b)+bc(c-b)]

<=>(c-a)(a-b).(ac+ab+bc)(c-b)

Answer 8

làm phép chi (lớp 8) mọi người giải chi tiết nha
cho t nhờ tí nha
mọi người ơi làm giúp e với. Ai làm đc câu nào vào trang của e gửi câu trả lời cho e nha. E cảm ơn

a: (4x² - 9y²): (2x - 3y)

b: (27x³ - 1) : (3x² - 1)

c: (8x³ + 1) : (4x² - 2x + 1)

d: (x² - 3x +xy - 3y): (x + y)

e: (6x³ - 7x² - x + 2): (2x + 1)

f: (x⁴ - x³ + x² + 3x) : (x² - 2x + 3)

Answer 9

<=> a^2.b^2.(a-b) + b^2.c^2.(b-c) + c^2.a^2.(c-a)

<=>a^2.b^2.(a-b) - b^2.c^2.(c-b) + c^2.a^2.(c-a)

<=>a^2.b^2.(a-b) - b^2.c^2.[(a-b)+(c-a)] + c^2.a^2.(c-a)

<=>a^2.b^2.(a-b) - b^2.c^2.(a-b) – b^2.c^2.(c-a) + c^2.a^2.(c-a)

<=>b^2.(a-b).(a^2-c^2) + c^2.(c-a).(a^2-b^2)

<=>b^2.(a-b).(a-c).(a+c) + c^2.(c-a).(a-b).(a+b)

<=>-b^2.(a-b).(c-a).(a+c) + c^2.(c-a).(a-b).(a+b)

<=>(c-a).(a-b).[ac^2+bc^2-ab^2-cb^2]

<=>(c-a).(a-b).[a(c^2-b^2)+bc(c-b)]

<=>(c-a)(a-b).[a(c-b)(c+b)+bc(c-b)]

<=>(c-a)(a-b).(ac+ab+bc)(c-b)