Question

因式分解 ，要过程。。

3x^3-12x
x^2(x-2y)+y^2(2y-x）
-16+p^4
9(a-b)^2-25(a+b)^2
a^5-a^3
m^2(x-y)+n^2(y-x)
y^2-二分之一y+十六分之一
4x^2 y^2-4xy+1
9m^2-24mn+16n^2
8a-4a^2 -4
(x-2）^2+10(x-2）+25
（a+b)^2- 6(a+b)+9
(z^2+1)^2-4z（z^2+1)+4z^2
(x+y)^3-4xy(x+y)

Answer 1

3x³-12x
=3x(x²-4)
=3x(x+2)(x-2)

x²(x-2y)+y²(2y-x)
=x²(x-2y)-y²(x-2y)
=(x-2y)(x²-y²)
=(x-2y)(x+y)(x-y)

-16+p⁴
=p⁴-16
=(p²+4)(p²-4)
=(p²+4)(p+2)(p-2)

9(a-b)²-25(a+b)²
=[3(a-b)+5(a+b)][3(a-b)-5(a+b)]
=(8a+2b)(-2a-8b)
=-4(4a+b)(a+4b)

a^5-a³
=a³(a²-1)
=a³(a+1)(a-1)

m²(x-y)+n²(y-x)
=m²(x-y)-n²(x-y)
=(x-y)(m²-n²)
=(x-y)(m+n)(m-n)

y² -y/2 +1/16
=(y- 1/4)² /完全平方公式，只一步。

4x²y²-4xy+1=(2xy-1)² /完全平方公式，只一步

9m²-24mn+16n²=(3m-4n)² /完全平方公式，只一步

8a-4a²-4
=-4(a²-2a+1)
=-4(a-1)²

(x-2)²+10(x-2)+25
=[(x-2)+5]²
=(x+3)²

(a+b)²-6(a+b)+9
=[(a+b)-3]²
=(a+b-3)²

(z²+1)²-4z(z²+1)+4z²
=[(z²+1)-2z]²
=[(z-1)²]²
=(z-1)⁴

(x+y)³-4xy(x+y)
=(x+y)[(x+y)²-4xy]
=(x+y)(x-y)²