分解因式:2m^3 - 8m(x+2)(x+4)+ x^2 -44(x-y)^2 - 2(y-x)^3x^2 (y^2
1个回答

1.2m^3 - 8m =2m(m^2-4)=2m(m-2)(m+2)

2.(x+2)(x+4)+ x^2 -4

=(x+2)(x+4)+(x-2)(x+2)

=(x+2)(2x+2)=2(x+2)(x+1)

3.4(x-y)^2 - 2(y-x)^3 =

4(x-y)^2 +2(x-y)^3=

(x-y)^2(4+2x-2y)

4.x^2 (y^2 - 1)+2x(y^2 - 1)+(y^2 - 1)=

(y^2 - 1)(x^2+2x+1)=(y^2 - 1)(x+1)^2

a(x-y)-b(y-x)+c(x-y)

=a(x-y)+b(x-y)+c(x-y)

=(x-y)(a+b+c

3 x^3 y - 6xy + 3y

=3y(x^3 - 2x + 1)

=3y(x^3 - x^2+ x^2 -2x + 1)

=3y(x-1)(x^2+x-1)

x^3 + 6x^2 - 27

=X立+3X方+(3X方-27)

=X方(X+3)+3(X+3)(X-3)

2a-b)^2+8ab

(2a-b)^2+8ab=4a^2-4ab+b^2+8ab

=4a^2+4ab+b^2

=(2a+b)^2

(x+2)(x+3)+ x^2 +4=X方+5X+6+X方+4

=2X方+5X+4

=(X+2)(2X+2)

xy-x-y+1

=x(y-1)-(y-1)

=(x-1)(y-1)

=(X+3)(X方+3X-9)

a^2 - 2ab + b^2 -1=(A-B)方-1

=(A-B+1)(A-B-1)

计算:(1-1/2^2)=(1-1/2)(1+1/2)=1/2*3/2

(1-1/3^2)=(1-1/3)(1+1/3)=2/3*4/3

...

(1-1/9^2)=8/9*10/9

(1-1/10^2)=9/10*11/10

(1-1/2^2)(1-1/3^2)(1-1/4^2)...(1-1/9^2)(1-1/10^2)

=1/2*3/2*2/3*4/3*...*8/9*10/9*9/10*11/10

=1/2*11/10

=11/20

2010^2 - 2009^2 + 2008^2 - 2007^2 +...+ 2^2 - 1^2=2011(2010-2009+2008_2007+...+2-1)=2011*1005=2021055

27^2-46*27+ 23^2

=27^2-2*23*27+ 23^2

=(27-23)^2=25

a^2 + b^2 + 2a-4b+5

=(a^2+ 2a+1)+( b^2-4b+4)

=(a+1)^2+(b-2)^2=0

a+1=0 b-2=0

a=-1 b=2

4a^2 + b^2 =4ab

4a^2 + b^2 -4ab=0 两边通除以非负数a^2

(b/a)^2-4b/a+4=0 b/a=2