Question

How would the expression x^3+18 be re written using the sum of cubes

Answer 1

Answer: are you sure it is 18, and not some number like 27?

Explanation:

the sum of cubes is a^3 + b^3 = (a+b) (a^2+ab+b^2)

the a and b must be able to be expressed in a cube form such as x^3, but there is no cube root of 18.

27 for example does have it. 3^3 because 3*3*3=27 so it could be expressed as X^3 and 3^3 which would follow that form above. X being the a and the 3 being the b. hope this helped, have a great day!

Answer 2

For this case we have that by definition, the sum of cubes is given by:

`a ^ 3 + b ^ 3 = (a + b) (a ^ 2-ab + b ^ 2)`

In this case, the expression
`x ^ 3 + 18`cannot be represented in this way.

But the expression
`x ^ 3 + 27` can be rewritten as:

`x ^ 3 + 3 ^ 3 = (x + 3) (x ^ 2-3x + 3 ^ 2) = (x + 3) (x ^ 2-3x + 9)`

Answer:

`x ^ 3 + 3 ^ 3 = (x + 3) (x ^ 2-3x + 9)`