Factoring 1 X to the fourth power of 2001X to the square of 2000X 2000X 2000

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Factoring 1 x to the fourth power 2001x squared 2000x 2000 bounty points: 0 - 14 days and 23 hours until the end of the question.

2 (6x 1) (2x 1) (3x 1) (x 1) x squared xy 6y squared x 13y 6

4 (x squared 1) (x 3) (x 5) 125 (x 1) (x 2) (x 3) (x 6) x squared.

Asked by: kokiajmy - Magic Apprentice 1 in total.

No points, no does.

The factoring is as follows:x^4+1

x^4+2x^2+1-2x^2

x^2+1)^2-2x^2

x^2+1)^2-(√2x)^2

x 2+1 + 2x) (x 2+1- 2x) uses the formula method and squared difference formula.

A number to the power of zero.

Any non-zero number to the power of 0 is equal to 1. Here's why.

Usually represents to the power of 3.

The 3rd power of 5 is 125, i.e. 5 5 5 = 125

The 2nd power of 5 is 25, i.e. 5 5 = 25

The power of 5 to the power of 5 is 5, i.e. 5 1 = 5

It can be seen that when n 0, the power of (n+1) of 5 becomes the power of 5 to the power of 5 needs to be divided by a 5, so the power of 5 can be defined as:

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x^4+x^2+1

x^4+2x^2+1）-x^2

x^2+1）^2-x^2

（x^2+1）+x］［（x^2+1）-x］=（x^2+x+1）（x^2-x+1）

Principles of Factorization:Defactoring a factor is an identity deformation of a polynomial, requiring that the left side of the equation must be a polynomial, and the result of defactoring the factor must be expressed as a product.

Each factor must be an integer, and the degree of each factor must be less than the number of the original polynomial. As a result, only parentheses are left at the end, and the factorization must be carried out until each polynomial can no longer be factored;

The first term of the resulting polynomial is generally positive. Extract the common factor in a formula, that is, reorganize through the formula, and then extract the common factor; The first coefficient in parentheses is generally positive.

Solution: You can use the method of adding items and splitting items:

x∧4+x∧2+1

x∧4+2x∧2+1）-x∧2

x∧2+1）∧2-x∧2

（x∧2+1）+x］［（x∧2+1）-x］=（x∧2+x+1）（x∧2-x+1）

Splitting 1+x 4, we get: 1+x 4=(1+x) (1-x +x 4) where (1+x) is a quadratic factor and (1-x +x 4) is a quadratic factor.

The result of this factorization has a wide range of applications in mathematics and physics, such as calculating the Coulomb potential in electromagnetic fields, magnetic induction intensity, etc.

Now let's deduce the Xunsun process of this factorization:1First, we use the square formula to write 1+x 4 as (1+x) 2x:

1+x^4=(1+x²)²2x²2.Then use the difference squared formula to split (1+x): 1+x 4=(1+x + 2x)(1+x - 2x3.).

Then we split the 2x term into two x: 1+x 4=(1+x +x 2)(1+x -x 2)4Combine the two lead Chang tall formulas:

1+x 4=(1+x +x 2)(1+x -x 2)=(1+x)(1-x +x 4) So, the factoring of 1+x 4 is (1+x)(1-x +x 4).

This factorization can be used to simplify expressions, or abstract complex problems into simple mathematical concepts, and is widely used in mathematics, physics, and engineering disciplines.

In short, the insolution is one of the very basic contents in mathematics, and I hope that through this example, you can master the method and application of factorization. <>

x to the fourth power + x to the square + 1 x to the fourth power + 2x to the square + 1 -x to the square (x squared 1) to the square of x.

x squared 1 x) (x squared 1-x).