因式分解(8) 送20分

1(x-y)2 -(x-z)2
=[(x-y)-(x-z)][(x-y)+(x-z)]
=(z-y)(x-y-z)

2. (a+b+c)2 -d2
=[(a+b+c)-d][(a+b+c)+d]
=(a+b+c-d)(a+b+c+d)

3. (3x+2)2 -(2x+1)2
=[(3x+2)-(2x+1)][(3x+2)+(2x+1)]
=(x+1)(5x+3)

4. 9y2 -(2x-y)2
=(3y)2 -(2x-y)2
=[(3y)+(2x-y)][(3y)-(2x-y)]

5. (x-3y)2 -(y-x)2
=[(x-3y)+(y-x)][ (x-3y)-(y-x)]
=(-2y)(2x-4y)
=-4y(x-2y)

6. (3x-y)2 -(5x-3y)2
=[(3x-y)-(5x-3y)][(3x-y)+(5x-3y)]
=(-2x+2y)(8x-4y)
=-8(x-y)(2x-y)

7. 25x2 -(x+2y+4z)2
= (5x)2 -(x+2y+4z)2
=[(5x)-(x+2y+4z)][ (5x)+(x+2y+4z)]
=(4x-2y-4z)(6x+2y+4z)
=4(2x-y-2z)(3x+y+2z)

8. 4x2 +4x+1
=(2x)2 +4x+1
=(2x+1)2

9. x2 +2x+1-y2
=(x+1)^2-y2
=[(x+1)-y][ (x+1)+y]
=(x-y+1)(x+y+1)

10. a2 -2ab+b2 -9x2
=(a-b)2 -(3x)2
=[(a-b)-(3x)][(a-b)+(3x)]
=(a-b-3x)(a-b+3x)

11. x2 -a2 -2ab-b2
=x2 -( a2 +2ab+b2 )
= x2 -(a+b)2
=[ x-(a+b)][x+(a+b)]
=(x-a-b)(x+a+b)

4. 9y2 -(2x-y)2
=(3y)2 -(2x-y)2
=[(3y)+(2x-y)][(3y)-(2x-y)]
=[2y+2x][4y-2x]
=4(y+x)(2y-x)