The cubic expansion of 1.A and b;

(a+b)^3

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

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

=a^3+2a^2b+ab^2+a^2b+2ab^2+b^3

=a^3+3a^2b+3ab^2+b^3。

If the cube of a number is equal to a, then this number is called the cube root or cube root of a, that is, if x 3 = a, then x is called the cube root of a, the cube root of a positive number is positive, the cube root of a negative number is negative, and the cube root of 0 is 0.

Second, the complete cubic formula:

Including the complete cubic sum formula and the complete cubic difference formula, the complete cubic sum (or difference) formula means that the cube of the sum (or difference) of two numbers is equal to three times the sum (or difference) of the cubic sum (or difference) of these two numbers and the square of each number multiplied by the sum (or difference) of another number.

Third, the cubic expansion of a-b:

(a-b)^3

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

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

=a^3-3a^2b+3ab^2-b^3。

Four, cubic summation formula:

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 their square sum and product, is equal to the cubic sum of these two numbers; The expression is: (a+b)(a? -ab+b？ )=a？ +b？ .

Because (a-b)? =a？ -3a2b+3ab？ -B?

So according to the exchange law, the cubic difference formula is obtained:

Answer? -B? =(a-b)？ -(-3a2b+3ab？ )

=(a-b)(a-b)？ +3ab(a-b)

=(a-b) [(a-b)？ +3ab]

=(a-b) [(a？ -2ab+b？ )+3ab]

=(a-b)(a？ +ab+b？ )。

Power exponent of verb (abbreviation of verb)

When the exponent of a power is negative, it is called "negative exponential power". The -r power of a positive number A (R is any positive number) is defined as the reciprocal of the R power of A. ..

For example:

2 to the 6th power = 2 6 = 2× 2× 2 = 4× 2× 2 = 8× 2× 2 =16× 2× 2 = 32× 2 = 64.

The fourth power of 3 = 3 4 = 3× 3× 3 = 9× 3× 3 = 27× 3 = 8 1.

As shown in the above formula, the 6th power of 2 is the multiplication of 6 2s, and the 4th power of 3 is the multiplication of 4 3s. If it is a relatively large number multiplication, you can also use calculation tools such as settlement calculator and computer to calculate.

Six, other formulas:

1, sum of squares formula:

(a+b)？

=(a+b)(a+b)

=a？ +ab+ab+b？

=a？ +2ab+b？ .

2. Variance formula:

(a-b)?

=(a-b)(a-b)

=a？ -ab-ab+b？

=a？ -2ab+b？ .