Question

Prove that (a + b + c) 3 − a 3 − b 3 − c 3 = 3 (a − b)(b − c)(c − a)

Answer 1

Answer:

Write the problem in a division-like format.

To do this:

Take the constant term of the divisor with the opposite sign and write it to the left.

Write the coefficients of the dividend to the right.

5x41x3−5x27x1−34x0−1

Step 1

Write down the first coefficient without changes:

511−57−34−1

Step 2

Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

511−55⋅1=5(−5)+5=07−34−1

Step 3

Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

511−55075⋅0=07+0=7−34−1

Step 4

Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).