(x^3-y^3)=(x-y)(x^2+y^2+xy)

This is the cubic difference formula, just remember it.

This formula is used in high school mathematics, plays an important role in mathematical research, and even in advanced mathematics and calculus. The sum of squares of two numbers plus the product of two numbers and then multiplied by the difference of two numbers, the product is equal to the cubic difference of two numbers.

Advanced certification:

Because (a-b) 3 = a 3-3a 2b+3ab 2-b 3.

So according to the law of exchange:

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

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

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

=(a-b) [(a-b)^2+3ab]

=(a-b) [(a^2-2ab+b^2)+3ab]

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

Prove:

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