R. D. Sharma Solutions for Chapter: Factorization of Algebraic Expressions, Exercise 5: VERY SHORT ANSWER TYPE QUESTIONS (VSAQs)

If $a+b+c=0$, then write the value of $a^3+b^3+c^3$.

If $a^2+b^2+c^2=250$ and $ab+bc+ca=3$, find $a+b+c$.

Write the value of ${25}^3-{75}^3+{50}^3$.

Write the value of ${48}^3-{30}^3-{18}^3$

Write the value of ${\left(\frac{1}{2}\right)}^3+{\left(\frac{1}{3}\right)}^3-{\left(\frac{5}{6}\right)}^3$.

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

If the factorized form of $x^4+x^2+25$ is $\left(x^2+k+mx\right)\left(x^2+k-mx\right)$, then find the value of $\left(k+m\right)$.

Factorize: $x^2-1-2a-a^2$.