Question

Factorise ab³+bc³+ca³+a²b²c²-a³b²-b³c²-c³a²-abc​

Answer 1

Step-by-step explanation:

ab^3-a^3b^2+bc^3-b^3c^2+ca^3-c^3a^2-a^2b^2c^2-abc

ab(a^2-b^2)+bc(b^2-c^2)+ca(c^2-a^2)+abc(abc-1)

(ab+bc+ca+abc)(a^2-b^2)(b^2-c^2)(c^2-a^2)(abc-1)

now, put a^2-b^2=0, b^2-c^2=0, c^2-a^2=0,abc-1=0

so, a^2=b^2, b^2=c^2,abc=1

(ab+bc+ca+abc)(b^2-b^2)(c^2-c^2)(a^2-a^2)(1)

(ab+bc+ca+abc)×0×0×0×1

(ab+bc+ca+abc)×0

=0. here is your answer.