Question

If a, b, c are any three integers then abc * (a ^ 3 - b ^ 3) * (b ^ 3 - c ^ 3) * (c ^ 3 - a ^ 3) is divisible by​

give me the correct answer with explanation i will make you brain list

Answer 1

Answer:

hii bro how are you

are u in class 11

bro please follow

Answer 2

Answer:

$\mathrm{Least\:Common\:Multiplier\:of\:}a,\:b,\:c,\:\cdot \left(a^3-b^3\right)\cdot \left(b^3-c^3\right)\cdot \left(c^3-a^3\right),\:by:\quad$

$a\left(a-b\right)\left(a^2+ab+b^2\right)b(b-c)(b^2+bc+c^2)c(c-a)(c^2+ac+a^2)y$

Step-by-step explanation:

$\left(a^3-b^3\right)\left(b^3-c^3\right)\left(c^3-a^3\right)$

$=\left(a-b\right)\left(a^2+ab+b^2\right)\left(b^3-c^3\right)\left(c^3-a^3\right)$

$=\left(a-b\right)\left(a^2+ab+b^2\right)\left(b-c\right)\left(b^2+bc+c^2\right)\left(c^3-a^3\right)$

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

$\mathrm{Factor\:}by$

$b\cdot \:y$

$\mathrm{Multiply\:each\:factor\:with\:the\:highest\:power:}$

$a\cdot \left(a-b\right)\cdot \left(a^2+ab+b^2\right)\cdot \:b\cdot \left(b-c\right)\cdot \left(b^2+bc+c^2\right)\cdot \:c\cdot \left(c-a\right)\cdot \left(c^2+ac+a^2\right)\cdot \:y$