Square difference formula: (a+b)(a-b)=a? -B?

Complete square formula: (a b)? =a？ 2ab+b？

Turn the formula upside down:

(a+b)(a-b)=a？ -B?

Answer? 2ab+b？ =? (A and B)?

It becomes factorization, so we call the method of factorization using square difference formula and complete square formula method factorization.

Example:

1、25- 16x？ =5? -(4x)？ =(5+4 times) (5-4 times)

2、p4- 1

=(p？ + 1)(p？ - 1)

=(p？ + 1)(p+ 1)(p- 1)

3、x？ + 14x+49

=x？ +2 7 x+7？

=(x+7)？

4 、( m-2n)？ -2(2n-m)(m+n)+(m+n)？

=(m-2n)？ +2(m-2n)？ (m+n)+(m+n)？

=[(m-2n)+(m+n)]？

=(2m-n)？

Extended data

note:

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

The "negative" here means "minus sign". If the first term of a polynomial is negative, it is generally necessary to put forward a negative sign to make the coefficient of the first term in brackets positive.

2. If each term of the polynomial contains a common factor, first extract this common factor, and then further decompose this factor;

It should be noted that when the whole term of a polynomial is a common factor, 1 should not be omitted in brackets after this common factor is put forward first; The common factor should be cleaned up at one time, and the polynomial in each bracket can't be decomposed.

3. If there is no common factor, then try to decompose it by formula and cross multiplication;

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

Baidu encyclopedia-factor decomposition