-25x^2+4因式分解(写步骤)因式分解:-81+a^4 4(x+1)^2-9 (3x+2y)^2-(2x+3y)^2x^2(a-1)+4(1-a)

问题描述:

-25x^2+4因式分解(写步骤)
因式分解:-81+a^4 4(x+1)^2-9 (3x+2y)^2-(2x+3y)^2
x^2(a-1)+4(1-a)

-25x^2+4
=-(25x^2-4)
=-(5x+4)(5x-4)
-81+a^4
=a^4-81
=(a^2+9)(a^2-9)
=(a^2+9)(a+3)(a-3)
4(x+1)^2-9
=[2(x+1)+3]*[2(x+1)-3]
=(2x+5)(2x-1)
(3x+2y)^2-(2x+3y)^2
=[(3x+2y)+(2x+3y)]*[(3x+2y)-(2x+3y)]
=(5x+5y)(x-y)
=5(x+y)(x-y)
x^2(a-1)+4(1-a)
=x^2(a-1)-4(a-1)
=(a-1)(x^2-4)
=(a-1)(x+2)(x-2)