Question

因式分解复习题

a^3-4a 1-25a^2 (a-b)(x-y)-(b-a)(x+y)
2m(3x-y)^2-3n(y-3x)^2 25(x+y)^2-16(x-y)^2 -0.001+49b^2
4m-m(3a-2)^2 x(a+b)+y(a+b) 2x(a-b)+b-a
4x^2-4x+1 x^2-1/2x+1/4 1+m+ m^2/4
25x^4+20x^2+4 49b^2+a^2-14ab -x^2+2xy-y^2

Answer 1

解：

a^3-4a
=a(a²-4)
=a(a+2)(a-2)

1-25a²
=(1+5a)(1-5a)

(a-b)(x-y)-(b-a)(x+y)
=(a-b)(x-y+x+y)
=2x(a-b)

2m(3x-y)²-3n(y-3x)²
=(2m-3n)(3x-y)²

25(x+y)²-16(x-y)²
=[5(x+y)+4(x-y)]*[5(x+y)-4(x-y)]
=(9x+y)(x+9y)

-0.01+49b²
=(7b+0.1)(7b-0.1)

4m-m(3a-2)²
=3a(4-3a)m

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

2x(a-b)+b-a
=(a-b)(2x-1)

4x²-4x+1
=(2x-1)²

x²-(1/2)x+1/4
此因式无法分解，请楼主核对题目。

1+m+m²/4
=(1+m/2)²

25x^4+20x²+4
=(5x²+2)²

49b²+a²-14ab
=(7b-a)²

-x²+2xy-y²
=-(x-y)²

不明白的请再问。

谢谢！