Identity , factorization

1.proof it is an identity.
(x+2)^2-(x-2)^2=8x
L.H.S. = (x+2 + x-2)[x+2 - (x-2)]
= 2x * 4
= 8x = R.H.S.
2.Factorize the following
4(x-2)^2+12(x-2)
= 4(x-2)[(x-2) + 3]
= 4(x-2)(x+1)
3.
5(x+y)^2-20(x+y)(x-y)+20(x-y)^2

Let x+y = a


x-y = b


5a^2 - 20ab + 20b^2


= 5(a^2 - 4ab + 4b^2)


= 5(a - 2b)^2


= 5[(x+y - 2(x-y)]^2


= 5(3y - x)^2

1.L.H.S=(x+2)2-(x-2)2
=[(x+2)-(x-2)][(x+2)+(x-2)]
=4(2x)
=8x
=R.H.S.
∴(x+2)2-(x-2)2=8x

2. 4(x-2)2+12(x-2)
=4(x-2)[(x-2)+3]
=4(x-2)(x+1)

3. 5(x+y)2-20(x+y)(x-y)+20(x-y)2
=[5(x+y)-10][(x+y)-2]
=(5x+5y-10)(x+y-2)

2009-10-11 18:42:10 補充：
=5(x+y-2)(x+y-2)
=5(x+y-2)^2