Factoring, formula method, factoring formula

Factorization: Formula method. Items of the same kind that can be merged should be merged.

The common methods of factorization include the common factor method, the formula method, the grouping decomposition method, and the cross multiplication method.

Either way, if there is a common factor, it is easier to mention the common factor first and then use the other method.

In junior high school, the formula method commonly used is the squared difference formula: a 2-b 2 = (a + b) (a - b).

The perfect square formula: a 2 + 2ab + b 2 = (a + b) 2 or a 2 - 2 ab + b 2 = (a - b) 2

In high school, there are also cube sum and difference formulas, sum and difference cube formulas, etc.

For example: am 2-an 2=a(m 2-n 2)=a(m+n)(m-n) (first mention the common factor a, and then use the square difference formula).

x 4-2x 2y 2+y 2=(x 2-y 2) 2=(x+y) 2(x-y) 2 (use the perfect squared formula first, then the squared difference formula).

x squared to the fourth power y - x to the fourth power y squared.

x²y²(y²-x²)

x²y²(y+x)(y-x)

x squared + y squared.

y+x)(y-x)

a+b) - 4a squared.

a+b+2a)(a+b-2a)

3a+b)(b-a)

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2ab: Question A is x, not x.

b is 2y and not (2y) squared.

So 2ab should be equal to 2·x·2y

This is to use a perfectly squared formula to break down the factor. Here 2ab, x and 2y are not squared, but twice the product.

The formulas commonly used in factoring are squared difference formula, perfect square formula, perfect cubic formula, cubic sum and cubic difference formula, etc. They use the multiplication formula in reverse.

When we need to factor a polynomial, using different formulas can help us complete the decomposition faster and more accurately. Here is an introduction to some commonly used factorization formulas:

1.The factorization formula for a quadratic trinomial: a 2-b 2=(a+b)(a-b), where a and b are arbitrary real numbers.

This formula can help us decompose a quadratic trinomial into the product of two quadratic binomials, and is usually used to simplify the solution of equations or equations.

2.The perfect square formula: a 2+2ab+b 2=(a+b) 2, where a and b are arbitrary real numbers.

This formula can help us break down a perfectly flat form into a square of a primary binomial, and is often used to solve simplified formulas or equations.

3.The formula for the square of the difference: a 2-2ab+b 2=(a-b) 2, where a and b are arbitrary real numbers.

This formula can help us decompose a difference into a square of a primary binomial, and is often used to simplify the solution of equations or equations.

4.The factorization formula for quadratic multinomial key beats: ax 2+bx+c=a(x-x 1)(x-x 2), where x 1 and x 2 are the two real roots of the equation ax 2+bx+c=0.

This formula allows us to decompose a quadratic polynomial into the product of two quadratic polynomials, which is usually used to solve quadratic equations or simplifications.

5.The factorization formula for cubic polynomials: ax 3+bx 2+cx+d=a(x-x 1)(x 2+px+q), where x 1 is a real root of the equation ax 3+bx 2+cx+d=0 and p and q are the real numbers to be determined.

This formula can help us decompose a cubic polynomial into the product of a primary and a quadratic polynomial, and is usually used to solve cubic equations or simplifications.

6.The factorization formula for the quadratonic polynomial: ax 4+bx 3+cx 2+dx+e=a(x-x 1)(x-x 2)(x 2+px+q), where x 1 and x 2 are the two real roots of the equation ax 4+bx 3+cx 2+dx+e=0, and p and q are the real numbers to be determined.

This formula allows us to decompose a quadratic polynomial into the product of a one-dimensional and a cubic polynomial, and is often used to solve quadratic equations or simplified equations.

The above is an introduction to some commonly used factorization formulas, which have a wide range of applications in fields such as algebra, mathematics, and physics. Mastering these formulas can help us solve various math problems more effectively. <>

Factoring Formula:

Square difference formula: (a+b)(a-b)=a-b.

The perfect square formula: (a b) = a 2ab + b.

Turn the formula upside down:

a+b)(a-b)=a²-b²。

a²±2ab+b²= a±b)²。

This becomes factoring, so we call the method of factoring using the squared difference formula and the perfect squared formula the formula formula.

Note: 1. If the first term of the polynomial is negative, the negative sign should be extracted first.

The "negative" here refers to the "negative sign". If the first term of the polynomial is negative, a negative sign is generally proposed so that the coefficient of the first term in parentheses is positive.

2. If each item of the polynomial contains a common factor, then the common factor is extracted first, and then the factor is further decomposed.

Note: When a whole term of a polynomial is a common factor, after proposing the common factor first, do not omit 1 in parentheses; Mention the common factor should be cleaned at once, and the polynomial in each parenthesis can no longer be decomposed.

3. If there is no common factor for each item, then you can try to use formulas and cross multiplication to decompose it.

4. If the above methods cannot be decomposed, try to decompose by grouping, splitting items, and supplementing items.

Factorization formula: (1) square difference formula a -b = (a + b) (a-b); (2) The perfect square formula a +2ab+b = (a+b); 3) The cube sum formula a +b = (a + b) (a -ab + b ) and so on.

The form of converting a polynomial into the product of several integers in a range is called factorization of the polynomial, also known as factorization of the polynomial.

Factorization mainly includes cross multiplication, undetermined coefficient method, double cross multiplication, symmetric polynomial, rotational symmetric polynomial method, coincidence theorem and other methods. In the competition, there are also splitting and adding and subtracting terms, changing the element method, long division, short division, division, etc.

1. Square difference formula: a -b = (a + b) (a-b).

(2) The perfect square formula a +2ab+b = (a+b);

3. Cube sum formula: a +b = (a + b) (a -ab + b).

4. Cubic deviation formula: a -b = (a-b) (a + ab + b).

5. The perfect cubic sum formula: a +3a b + 3ab +b =(a + b).

6. The formula of complete cubic variance: a -3a b + 3ab -b = (a-b).

7. Three perfect square formulas: a + b + c + 2ab + 2bc + 2ac = (a + b + c).

8. The formula for the sum of the cubes of the three terms: a + b + c -3abc = (a + b + c) (a + b + c -ab-bc-ac).

Factorization: Formula method. Items of the same kind that can be merged should be merged.

So much, the homework left by the teacher, right? Let's do it yourself. If you don't know how to ask questions, ask questions.

One; Square Difference Formula.

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

Two; Perfectly squared formula.

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

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

Three; Sum of cubes (difference).

The difference between two numbers multiplied by their sum of squares and their product is equal to the cubic difference of the two numbers.

i.e. a 3-b 3 = (a-b) (a 2 + ab + b 2) proves as follows: a 3-b 3 = a 3-3a 2b + 3ab 2-b 3 so a 3-b 3 = (a - b) a 3-[-3(a 2) b + 3ab 2] = (a - b) (a - b) 2 + 3 ab (a-b).

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

Five; Cross multiplication formula.

Cross multiplication can factor certain quadratic trinomials. It is important to pay attention to the symbols of the various coefficients.

x+a)(x+b)=x 2+(a+b)x+abCitation]

Factorization: Formula method. Items of the same kind that can be merged should be merged.

Decomposition of the hidden cover due to the stove staring: the formula method. Similar items that can be merged should be merged.