Form 2 Maths...Ｈeｌｐ!

1) 4x^(4) - 180x^(2) - 16x^(3)
=(4x^2)(x^2-4x-45)
直式:
x-9
x+5
-------------
x^2-4x-45
So,4x^(4) - 180x^(2) - 16x^(3)=4x^2(x-9)(x+5)

2) -15c^(2)d^(3) + 6cd^(3) + 9d^(3)
=-3d^3(5c^2-2c-3)
直式:
5c+3
c-1
--------------
5c^2-2c-3
So,-15c^(2)d^(3) + 6cd^(3) + 9d^(3)=-3d^3(5c+3)(c-1)

3) 9a^(2) + 20(a-c)^(2) - 36a(a-c)
=9a^2+20a^2-40ac+20c^2-36a^2+36ac
=-7a^2-4ac+20c^2
=-(7a^2+4ac-20c^2)
直式:
7a-10c
a+2c
--------------
7a^2+4ac-20c^2
So,9a^(2) + 20(a-c)^(2) - 36a(a-c)=-(7a-10c)(a+2c)

4) x^(2)y – 2xy^(2) + y^(3) - 9y
=y[(x^2-2xy+y^2)-9]
=y[(x-y)^2-3^2]*
=y(x-y+3)(x-y-3)**
*(公式:x^2-2xy+y^2=(x-y)^2)
**(公式:a^2-b^2=(a+b)(a-b))

5) (a+2)^(2) + 4a + 2a^(2) + 1
=a^2+4a+4+4a+2a^2+1
=3a^2+8a+5
直式:
3a+5
a+1
---------------
3a^2+8a+5
So,(a+2)^(2) + 4a + 2a^(2) + 1=(3a+5)(a+1)