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a) x3+y3+z3-3xyz
=(x+y)3+z3-3x2y-3xy2-3xyz
=(x+y+z).[(x+y)2+(x+y).z+z2]-3xy.(x+y+z)
=(x+y+z)(x2+2xy+y2+zx+zy+z2)-3xy.(x+y+z)
=(x+y+z)(x2+2xy+y2+zx+zy+z2-3xy)
=(x+y+z)(x2+y2+zx+zy+z2-zy)
b)a2(b-c)+b2(c-a)+c2(a-b)
=a2b-a2c+b2c-b2a+c2a-c2b
=(a2b-c2b)+(-a2c+c2a)+(b2c-b2a)
=b.(a2-c2)-ac.(a-c)-b2.(a-c)
=b.(a+c)(a-c)-ac.(a-c)-b2.(a-c)
=(a-c)[b.(a+c)-ac-b2]
=(a-c)(ab+bc-ac-b2)
=(a-c)[(ab-ac)+(bc-b2)]
=(a-c)[a.(b-c)-b.(b-c)]
=(a-c)(b-c)(a-b)
\(a\left(b^2-c^2\right)-b\left(c^2-a^2\right)+c\left(a^2-b^2\right)\)
\(=a\left(b^2-c^2\right)-b\left(c^2-a^2\right)-c\left[\left(b^2-c^2\right)+\left(c^2-a^2\right)\right]\)
\(=a\left(b^2-c^2\right)-b\left(c^2-a^2\right)-c\left(b^2-c^2\right)-c\left(c^2-a^2\right)\)
\(=\left(b^2-c^2\right)\left(a-c\right)-\left(c^2-a^2\right)\left(b +c\right)\)
\(=\left(b+c\right)\left(b-c\right)\left(a-c\right)-\left(c-a\right)\left(a+c\right)\left(b+c\right)\)
\(=\left(a-c\right)\left(b+c\right)\left(b-c+a+c\right)\)
\(=\left(a+b\right)\left(b+c\right)\left(a-c\right)\)
Bn tham khảo lời giải ở câu này nha
https://olm.vn/hoi-dap/question/705592.html
(a2 - b2 -c2 )2 -4a2b2
= (a2 -b2 -c2 )2 - (2ab)2
= (a2 -b2 - c2 -2ab)( a2 -b2-c2 +2ab)