If x=(1111)_{2}, y=(1001)_{2} and z=(110)_{2}, then what is x^{3}-y^{3}-z^{3}-3xyz equal to?
- A. (1111001)_{2}
- B. (1001111)_{2}
- C. (1)_{2}
- D. (0)_{2} ✓
Correct Answer: D. (0)_{2}
Explanation
x = 15, y = 9, z = 6 in decimal. Since x = y + z, we have x + (-y) + (-z) = 0. The expression is x^3 + (-y)^3 + (-z)^3 - 3x(-y)(-z), which is identically 0 when the sum of variables is 0.
Related questions on Algebra
- How many four-digit natural numbers are there such that <strong>ALL</strong> of the digits are odd?
- What is \sum_{r=0}^{n}2^{r}C(n,r) equal to ?
- If different permutations of the letters of the word 'MATHEMATICS' are listed as in a dictionary, how many words (with or without meaning) a...
- Consider the following statements : 1. If f is the subset of Z\times Z defined by f=\{(xy,x-y);x,y\in Z\}, then f is a function from...
- For how many quadratic equations, the sum of roots is equal to the product of roots?