Question

without actually calculating the cubs, find the value of each of the following. (I) (-12)3+(9)3+(3)3q
Please urgent ​

Answer 1

Answer:

$-972$

Step-by-step explanation:

$(-12)^{3} +(9)^{2} +(3)^{3}$

We know that $a^{3} +b^{3} +c^{3} -3abc = (a+b+c)(a^{2} +b^{2} +c^{2} - ab - bc - ac)$

But there is a special condition to the above formula:-

if $a + b + c = 0$ then $a^{3} +b^{3} +c^{3} = 3abc$

In this case $a = -12$, $b = 9$ and $c = 3$

Since, $-12 + 9 + 3 = 0$

$(-12)^{3} + (9)^{3} + (3)^{3} = 3(-12)(9)(3)$

⇒ $-972$