Cubic sum formula: (a+b)(a? -ab+b？ )=a？ +b？ .

Cubic sum formulas are sometimes used in mathematical operations. The literal expression of this formula is: the sum of two numbers multiplied by the difference between the sum of their squares and the product is equal to the cubic sum of these two numbers.

Cubic difference formula is also one of the commonly used formulas in mathematics. 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.

The cubic difference formula proves that:

So according to the law of exchange:

a3-b3=(a-b)3-(-3a2b+3ab2)

=(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) [(a2-2ab+b2)+3ab]

=(a-b)(a2+ab+b2)

Proof: a3-b3=(a-b)(a2+ab+b2)