因式分解(9x^2-4y^2+20yz-25z^2)/(6x-4y+10z)全是因式分解1.4y^2-20yz+25z^2承上题9x^2-4y^2+20yz-25z^2承上题(9x^2-4y^2+20yz-25z^2)/(6x-4y+10z)2.x^2-6x+8承上题-2(3a^2+a)^2+12(3a^2+a)-16

Question

因式分解 (9x^2-4y^2+20yz-25z^2)/(6x-4y+10z)
全是因式分解
1.4y^2-20yz+25z^2
承上题 9x^2-4y^2+20yz-25z^2
承上题 (9x^2-4y^2+20yz-25z^2)/(6x-4y+10z)
2.x^2-6x+8
承上题 -2(3a^2+a)^2+12(3a^2+a)-16

Answer 1

1.4y^2-20yz+25z^2
=(2y)^2-2*2y*5z+(5z)^2
=(2y-5z)^2
9x^2-4y^2+20yz-25z^2
=9x^2-(4y^2-20yz+25z^2)
=(3x)^2-(2y-5z)^2
=(3x-2y+5z)(3x+2y-5z)
(9x^2-4y^2+20yz-25z^2)/(6x-4y+10z)
=(3x-2y+5z)(3x+2y-5z)/[2(3x-2y+5z)]
=3x+2y-5z
2.x^2-6x+8
=(x-2)(x-4)
-2(3a^2+a)^2+12(3a^2+a)-16
=-2[(3a^2+a)^2-6(3a^2+a)+8]
=-2[(3a^2+a)-2][(3a^2+a)-4]
=-2(3a^2+a-2)(3a^2+a-4)
=-2(3a-2)(a+1)(3a+4)(a-1)