(Z的平方—X的平方—Y的平方)的平方—4乘以X的平方乘以Y的平方 因式分解a的平方b的平方—7ab+10

问题描述:

(Z的平方—X的平方—Y的平方)的平方—4乘以X的平方乘以Y的平方 因式分解
a的平方b的平方—7ab+10

4x2y2-(x2+y2-z2)2=[2xy-(x2+y2-z2)][2xy+(x2+y2-z2)]=[z^2-(x-y)^2][(x+y)^2-z^2]=(z+x-y)(z-x+y)(x+y+z)(x+y-z)=x+y+z)(x+y-z)(x-y+z)(z-x+y)
a^2b^2-7ab+10
=a^2b^2-2ab-5ab+10
=ab(ab-2)-5(ab-2)

=(ab-5)*(ab-2)

(z^2-x^2-y^2)^2-4x^2y^2
=(z^2-x^2-y^2+2xy)(z^2-x^2-y^2-2xy)
=[(z^2-(x-y)^2][z^2-(x+y)^2]
=(z+x-y)(z-x+y)(z+x+y)(z-x-y)
a^2b^2-7ab+10
=(ab-5)(ab-2)

1、=(z²-x²-y²)²-(2xy)²=(z²-x²-y²+2xy)(z²-x²-y²-2xy)=[z²-(x²-2xy+y²)][z²-(x²+2xy+y²)]=[z²-(x-y)²][z²-...

(Z的平方—X的平方—Y的平方)的平方—4乘以X的平方乘以Y的平方
=(z^2-x^2-y^2)^2-4x^2y^2
=(z^2-x^2-y^2)-(2xy)^2
=(z^2-x^2-y^-2xy)(z^2-x^2-y^2+2xy)
=[z^2-(x^2+y^2+2xy)][z^2-(x^2-2xy+y^2)]
=[z^2-(x+y)^2][z^2-(x-y)^2]
=(z-x-y)(z+x+y)(z-x+y)(z+x-y)
a的平方b的平方—7ab+10
=(ab)^2-7ab+10
=(ab)^2-(5+2)ab+5*2
=(ab-5)(ab-2)