Question

Write the value of ${30}^3+{20}^3-{50}^3.$

Answer 1

Finding the value of the given expression:

Let $a=30,b=20andc=-50$

Using identity, $a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)$

If $a+b+c=0$ then $a^3+b^3+c^3=3abc$

$a+b+c=30+20-50=0$

$$\begin{gathered} So,{30}^3+{20}^3+{(-50)}^3=3\left(30\right)\left(20\right)(-50) \\ =-90000 \end{gathered}$$

Hence, the value of the expression ${30}^3+{20}^3-{50}^3$ is $-90000.$