Question

Use the identity below to complete the tasks:

a^3 - 63 = (a - b)(a^2 + ab + b^2)
When using the identity for the sum of two cubes to factor 12526 - 26, what is a? What is b?

Answer 1

To factor the difference of two cubes 12526 - 26, we consider the closest perfect cubes which are 23^3 and 3^3, resulting in values of a = 23 and b = 3. This gives us the factored form using the identity a^3 - b^3 = (a - b)(a^2 + ab + b^2).

Step-by-step explanation:

To factor the difference of two cubes, 12526 - 26, we can use the given identity a3 - b3 = (a - b)(a2 + ab + b2). First, we need to express both numbers as cubes of two smaller numbers.

In this case, 12526 is the cube of 23 because 233 = 12167, and 26 is the cube of 3 because 33 = 27. However, there seems to be a slight error in the given expression since 12526 - 26 does not exactly yield a difference of two whole cubes. If we correct this to 12167 - 27, then we are dealing with perfect cubes (233 - 33).

By applying the identity to the corrected expression, we get a = 23 and b = 3. The factorized form of the expression will then be (23 - 3)(232 + 23*3 + 32).