Given a set of data \(x = \{2, 4, 6, 8, 10\}\), calculate the sum of cubes and then factorize the result.
Answer
Step 4: According to the formula of factorizing a sum of cubes \(a^3 + b^3 = (a+b)(a^2 - ab + b^2)\), we can write \(1800 = (2 + 3 + 5)((2^2 - 2*3 + 3^2) + (2^2 - 2*5 + 5^2) + (3^2 - 3*5 + 5^2))\).
Step 1 ：Step 1: First, we calculate the cube of each number in the set. The cubic of a number is the number multiplied by itself twice. So, the cube of each number in the set is \(2^3 = 8\), \(4^3 = 64\), \(6^3 = 216\), \(8^3 = 512\), \(10^3 = 1000\).
Step 2 ：Step 2: We add all these cubes together to get the sum of cubes. So, the sum is \(8 + 64 + 216 + 512 + 1000 = 1800\)
Step 3 ：Step 3: Now we factorize the sum of cubes. The sum is 1800, which can be expressed as \(2^3 * 3^3 * 5^3\).
Step 4 ：Step 4: According to the formula of factorizing a sum of cubes \(a^3 + b^3 = (a+b)(a^2 - ab + b^2)\), we can write \(1800 = (2 + 3 + 5)((2^2 - 2*3 + 3^2) + (2^2 - 2*5 + 5^2) + (3^2 - 3*5 + 5^2))\).
