分解因式：（1）18x^3-27x^4-3x^2 (2)x^4-18x^3+81 16a^2b^4-8ab^2c^2+c^4 (4)9(2x-y)^2-6(2x-y)+1分解因式：（1）18x^3-27x^4-3x^2 (2)x^4-18x^3+81 (3)16a^2b^4-8ab^2c^2+c^4 (4)9(2x-y)^2-6(2x-y)+1

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^4 (4)9(2x-y)^2-6(2x-y)+1
分解因式：（1）18x^3-27x^4-3x^2 (2)x^4-18x^3+81
(3)16a^2b^4-8ab^2c^2+c^4 (4)9(2x-y)^2-6(2x-y)+1

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