Question

Представьте выражение в виде суммы кубов.   а) x^3+n^3= b) p^9+64=  c) 8m^6+n^9=

Answer 1

a) x^3 + n^3 = b) p^9 + 64 = c) 8m^6 + n^9

a) The expression x^3 + n^3 can be represented as the sum of cubes. This is a special case of factoring called the sum of cubes. The sum of cubes formula states that x^3 + n^3 can be factored as (x + n)(x^2 - xn + n^2).

b) The expression p^9 + 64 can also be represented as the sum of cubes. In this case, we can rewrite 64 as 4^3. So, p^9 + 64 becomes p^9 + 4^3. Using the sum of cubes formula, we can factor it as (p^3 + 4)(p^6 - 4p^3 + 16).

c) Lastly, the expression 8m^6 + n^9 can also be represented as the sum of cubes. However, it is not a simple sum of two cubes. In this case, we cannot directly apply the sum of cubes formula. Instead, we need to find a way to rewrite it in a form that can be factored using the sum of cubes formula.