Maths 因式分解

a) x2 + 2x + 1
=(x+1) 2

b) 4x2 + 4x + 1
=(2x) 2+2(2x)(1)+1
=(2x+1) 2

c) x2 + 6x + 8
=x2+6x+9-1
=(x+3) 2-1
=[(x+3)-1] [(x+3)+1]
=(x+2)(x+4)

d) x2 - x - 12
=(x-4)(x+3)

e) 6x2 + 5x - 6
=(3x-2)(2x+3)

f) 2a2 - 32
=2(a2-16)
=2(a2-42)
=2(a-4)(a+4)

g) (a+b)2 – 9
=(a+b)2 – 32
=[(a+b)-3] [(a+b)+3]

h) x4y2z8 - x2
=x2(x2y2z8-1)
=x2[(xyz4)2-1]
= x2[(xyz4)-1] [(xyz4)+1]
= x2(xyz4-1) (xyz4+1)