which expression is a difference of cubes?\n$x^{6}-6$\n$x^{6}-8$\n$x^{8}-6$\n$x^{8}-8$
which expression is a difference of cubes?\n$x^{6}-6$\n$x^{6}-8$\n$x^{8}-6$\n$x^{8}-8$
Answer
Explanation:
Step1: Recall the form of difference of cubes
The difference - of - cubes formula is $a^{3}-b^{3}$. We need to check if the given expressions can be written in this form.
Step2: Analyze each option
- For $x^{6}-6$, $x^{6}=(x^{2})^{3}$, but 6 is not a perfect cube.
- For $x^{6}-8$, $x^{6}=(x^{2})^{3}$ and $8 = 2^{3}$, so $x^{6}-8=(x^{2})^{3}-2^{3}$, which is in the form of $a^{3}-b^{3}$ with $a = x^{2}$ and $b = 2$.
- For $x^{8}-6$, $x^{8}=(x^{\frac{8}{3}})^{3}$ (not a polynomial - like form we usually consider in basic algebra) and 6 is not a perfect cube.
- For $x^{8}-8$, $x^{8}=(x^{\frac{8}{3}})^{3}$ (not a polynomial - like form we usually consider in basic algebra) and 8 is a perfect cube but the first term is not in a proper cubic form for our basic difference - of - cubes concept.
Answer:
$x^{6}-8$