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

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

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

= (ab - b - a + 1)(c - 1) 

= (a - 1).(b - 1).(c - 1)   

$A=8abc+4\left(ab+bc+ca\right)+2\left(a+b+c\right)+1$

A = 8abc + 4ab + 4bc + 4ca + 2a + 2b + 2c + 1

$A=\left(8abc+4ab\right)+\left(4bc+2b\right)+\left(4ca+2a\right)+\left(2c+1\right)$

$A=4ab\left(2c+1\right)+2b\left(2c+1\right)+2a\left(2c+1\right)+\left(2c+1\right)$

$A=\left(2c+1\right)\left(4ab+2a+2b+1\right)$

$A=\left(2c+1\right)\left[2a\left(2b+1\right)+\left(2b+1\right)\right]$

$A=\left(2a+1\right)\left(2b+1\right)\left(2c+1\right)$

a: =(x+y)^3+z^3-3xy(x+y)-3xyz

\(=\left(x+y+z\right)\left[\left(x+y\right)^2-z\left(x+y\right)+z^2\right]-3xy\left(x+y+z\right)\)

\(=\left(x+y+z\right)\left(x^2+2xy+y^2-xz-yz+z^2-3xy\right)\)

\(=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-xz-yz\right)\)

b: \(=\left(x+y+y-z\right)^3-3\left(x+y\right)\left(y-z\right)\left(x+y+y-z\right)+\left(z-x\right)^3\)

\(=\left(x-z\right)^3+\left(z-x\right)^3-3\left(x+y\right)\left(y-z\right)\left(x-z\right)\)

\(=-3\left(x+y\right)\left(y-z\right)\left(x-z\right)\)

c: \(=\left(x^2+x\right)^2+3\left(x^2+x\right)+2-12\)

\(=\left(x^2+x\right)^2+3\left(x^2+x\right)-10\)

=(x^2+x+5)(x^2+x-2)

=(x^2+x+5)(x+2)(x-1)

d: =b^2c+bc^2+ac^2-a^2c-a^2b-ab^2

=b^2c-b^2a+bc^2-a^2b+ac^2-a^2c

=b^2(c-a)+b(c^2-a^2)+ac(c-a)

=(c-a)(b^2+ac)+b(c-a)(c+a)

=(c-a)(b^2+ac+bc+ba)

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

=(c-a)[b(b+c)+a(b+c)]

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

Ta có: \(D=ab\left(a+b\right)+bc\left(b+c\right)+ca\left(c+a\right)+3abc\)

\(=a^2b+ab^2+b^2c+bc^2+ac^2+a^2c+3abc\)

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

ai biết trả lời nhanh hộ mình nha! Mình k đúng cho!

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

bạn viết đề sai kìa bạn

sửa đề thành \(ab\left(a+b\right)+bc\left(b+c\right)+ca\left(c+a\right)+2abc\)

                    \(=ab\left(a+b\right)+b^2c+bc^2+c^2a+ca^2+2abc\)

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

                      \(=ab\left(a+b\right)+bc\left(a+b\right)+c^2\left(a+b\right)+ac\left(a+b\right)\)

                      \(=\left(a+b\right)\left(ab+bc+a^2+ca\right)\)

                      \(=\left(a+b\right)\left[\left(ab+bc\right)+\left(c^2+ac\right)\right]\)

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

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

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

(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)

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

\(=a^2b+ab^2-b^2c-bc^2+ca^2+c^2b+abc\)

\(=a^2b+ab^2-b^2c+a^2c+abc\)

       Đến đây thì mk chịu