= (abc - ab) + (a - ca) + (b - bc) + (c -1) = ab.(c -1) - a.(c - 1) - b(c -1) + (c -1) = (c -1).(ab - a - b  + 1)

abc-(ab+bc+ca)+(a+b+c)-1

=abc-ab-bc-ca+a+b+c-1

=(abc-ab)+(-bc+b)+(-ca+a)+(c-1)

=ab.(c-1)-b.(c-1)-a.(c-1)+(c-1)

=(c-1)(ab-b-a+1)

=(c-1)[b.(a-1)-(a-1)]

=(c-1)(a-1)(b-1)

= (abc - ab) + (a - ca) + (b - bc) + (c -1)

= ab.(c -1) - a.(c - 1) - b(c -1) + (c -1)

= (c -1).(ab - a - b  + 1)

\(A=\left(a+b+c\right).\left(bc+ca+ab\right)-abc\\ =abc+b^2c+bc^2+a^2c+abc+ac^2+a^2b+ab^2+abc-abc\\ =\left(b^2c+bc^2\right)+\left(a^2b+a^2c\right)+\left(ac^2+abc\right)+\left(ab^2+abc\right)\\ =bc\left(b+c\right)+a^2\left(b+c\right)+ac\left(b+c\right)+ab\left(b+c\right)\\ =\left(b+c\right)\left(bc+a^2+ac+ab\right)\\ =\left(b+c\right)\left[a\left(a+b\right)+c\left(a+b\right)\right]=\left(b+c\right)\left(a+c\right)\left(a+b\right)\)

(a + b + c)(bc + ca + ab) − abc

=(a + b)(bc + ca + ab) + c(bc + ca + ab) − abc

=(a + b)(bc + ca + ab)+ abc + c²(a + b) − abc

=(a + b)(bc + ca + ab + c²)

=(a + b)(b + c)(c + a)

(a+b+c)(ab+bc+ca)−abc

=(a+b)(ab+bc+ac)+c(ab+bc+ca)−abc

=(a+b)(ab+bc+ca)+abc+c2(a+b)−abc

=(a+b)(ab+bc+ca+c2)

=(a+b)(b+c)(c+a)

nguồn: https://h7.net/hoi-dap/toan-8/phan-h-a-b-c-ab-bc-ca-abc-thanh-nhan-tu--faq429360.html

Tham khảo tại đây nhé bạn Nguyễn Hà Anh

https://olm.vn/hoi-dap/detail/10986837094.html

dòng thứ 3 và thứ 4 là c² nhé, ko phải c2

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

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

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

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

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

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

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

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

mình làm vội, có chỗ nào sai bạn thông cảm nha

a) 4x² - 3x - 1 = 3x² -3x + x² -  1= 3x(x-1) + (x-1)(x+1) = (x-1)(3x +x+1)= (x-1)(4x+1)

b) chưa biết làm :)

b) ab(a-b)+bc(b-c)+ca(c-a)

=ab(a-b)-bc(c-b)+ac(c-a)

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

=ab(a-b)-bc(a-b)-bc(c-a)+ac(c-a)

=(a-b)(ab-bc)+(c-a)(ac-bc)

=b(a-b)(a-c)-(a-c)c(a-b)

=(a-c)(a-b)(b-c)