Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a3(c - b2) + b3(a - c2) + c3(b - a2) + abc(abc - 1)
= a3c - a3b2 + ab3 - b3c2 + bc3 - a2c3 + a2b2c2 - abc
= a2b2c2 - b3c2 - (a2c3 - bc3) - (a3b2 - ab3) + (a3c - abc)
= b2c2(a2 - b) - c3(a2 - b) - ab2(a2 - b) + ac(a2 - b)
= (a2 - b)(b2c2 - c3 - ab2 + ac) = (a2 - b)[c2(b2 - c) - a(b2 - c)] = (a2 - b)(b2 - c)(c2 - a)
a3(c - b2) + b(a - c2) + c3(b - a2) + abc(abc - 1)
= a3c - a3b2 + ab3 - b3c2 + c3b - a2c3 + a2b2c2 - abc
= (a2b2c2 - b3c2) + (a3c - abc) - (a3b2 - ab3) - (a2c3 - c3b)
= b2c2(a2 - b) + ac(a2 - b) - ab2(a2 - b) - c3(a2 - b)
= (a2 - b)(b2c2 + ac - ab2 - c3)
= (a2 - b)[(b2c2 - c3) - (ab2 - ac)]
= (a2 - b)[c2(b2 - c) - a(b2 - c)]
= (a2 - b)(c2 - a)(b2 - c)
\(\left(a+b\right)\left(a^2-b^2\right)+\left(b+c\right)\left(b^2-c^2\right)+\left(c+a\right)\left(c^2-a^2\right)\)
\(=\left(a+b\right)\left(a^2-b^2\right)-\left(b+c\right)\left[c^2-a^2+a^2-b^2\right]+\left(c+a\right)\left(c^2-a^2\right)\)
\(=\left(a+b\right)\left(a^2-b^2\right)-\left(b+c\right)\left(c^2-a^2\right)-\left(b+c\right)\left(a^2-b^2\right)+\left(c+a\right)\left(c^2-a^2\right)\)
\(=\left(a^2-b^2\right)\left(a+b-b-c\right)+\left(c^2-a^2\right)\left(c+a-b-c\right)\)
\(=\left(a-b\right)\left(a+b\right)\left(a-c\right)+\left(c-a\right)\left(c+a\right)\left(a-b\right)\)
\(=\left(a-b\right)\left(a-c\right)\left(a+b-c-a\right)\)
\(=\left(a-b\right)\left(a-c\right)\left(b-c\right)\)
Chúc bạn học tốt.
A = a^2b+ab^2+b^2c+bc^2+c^2a+ca^2+3abc
= (a^2b+ab^2+abc)+(b^2c+bc^2+abc)+(c^2a+ca^2+abc)
= (a+b+c).(ab+bc+ca)
k mk nha
( a + b ) ( b + c ) ( c + a ) + abc
= ( ab + ac + b^2 + bc ) ( c + a ) + abc
= ( c + a ) ( ab + ac + b^2 + bc ) + abc
= abc + ac^2 + b^2c + bc^2 + a^2b + a^2c + ab^2 + abc + abc
= 3abc + a . c^2 + b^2 . c + b . c^2 + a^2 . b + a^2 . c + a . b^2
= 3abc + c^2( a + b ) + b^2( c + a ) + a^2 ( b + c )