The following polynomials can be decomposed by complete square A.x²+1 B.x²+2x-1 C.x²+x+1 D.x²+4x+4 What is the factorization of the following polynomials in Liangshan in 2012 A.x²+y² B.-x²-y² C.-x²+2xy-y² D.x²-xy+y²

The following polynomials can be decomposed by complete square A.x²+1 B.x²+2x-1 C.x²+x+1 D.x²+4x+4 What is the factorization of the following polynomials in Liangshan in 2012 A.x²+y² B.-x²-y² C.-x²+2xy-y² D.x²-xy+y²

(1) Choose D
The complete square form is a trinomial form in which two square terms have the same sign
D.x²+4x+4=(x+2)²
（2）
Choose C
C.-x²+2xy-y²=-(x²-2xy+y²)=-(x-y)²

Which of the following polynomials is the complete square? Factorize the complete square:
(1）m^2+4m+4;
(2)m^2n^2-4+4mn;
(3)x+1+x^2/4;
(4)9p^2-24pq+16q^2

(1）m^2+4m+4
=（m＋2）²
(2) M ^ 2n ^ 2-4 + 4Mn; not a complete square
(3)x+1+x^2/4;
=(x／2＋1)²
(4)9p^2-24pq+16q^2
=(3p－4q)²

Can the following polynomials be factorized by the adjustment formula? Why?
（1）x²+y² （2）x²-y² (3)-x²+y² (4)-x²-y²

(1) X & # 178; + Y & # 178; is the simplest, so we can't decompose the factor any more
(2) X & # 178; - Y & # 178; can be decomposed by the square difference formula
x^2-y^2=(x+y)(x-y)
(3) - X & # 178; + Y & # 178; can be decomposed by the square difference formula
-x^2+y^2=y^2-x^2=(y+x)(y-x)
(4) - X & # 178; - Y & # 178; cannot be decomposed by the square difference formula
What can be decomposed by the square difference formula conforms to its prototype: x ^ 2-y ^ 2 = (x + y) (X-Y)

The common factor of polynomial n (m-n) - 2 (n-m) is

n(m-n)-2(n-m)
=n(m-n)+2(m-n)
So the common factor is m-n