Question

分解因式：（1）18x^3-27x^4-3x^2 (2)x^4-18x^3+81 16a^2b^4-8ab^2c^2+c

Answer 1

18x^3-27x^4-3x^2

=-3x^2(-6x+9x^2+1)

=-3x^2(9x^2-6x+1)

=-3x^2(3x-1)^2

x^4-18x^2+81

=(x^2)^2-2*x^2*9+9^2

=(x^2-9)^2

=(x+3)^2(x-3)^2

16a^2b^4-8ab^2c^2+c^4

=(4ab^2)^2-2*(4ab^2)*c^2+(c^2)^2

=(4ab^2-c^2)^2

9(2x-y)^2-6(2x-y)+1

=[3(2x-y)]^2-2*3(2x-y)+1

=[3(2x-y)-1]^2

=(6x-3y-1)^2