F.2 Identity

(2x-A)(2x+4)-Bx+25=(x-C)^2+Cx^2
lhs=(2x-a)(2x+a)-bx+25
=4x^2-a^2-bx+25

rhs=(x-C)^2+cx^2
=x^2-2cx+c^2+cx^2
=x^2(1+c)+c^2-2cx

from there,
1+c=4
c=3

b=6
c^2=-a^2+25
9=25-a^2
16=a^2
a=4

conform:
lhs=(2x-A)(2x+4)-Bx+25
=(2x-4)(2x+4)-6x+25
=4x^2-16-6x+25
=4x^2-6x+9
=(2x)^2-3^2
rhs=(x-C)^2+Cx^2
=(x-3)^2+3x^2
=x^2-6x+9+3x^2
=4x^2-6x+9
=(2x)^2-3^2
beacuse lhs=rhs
so (2x-A)(2x+4)-Bx+25≡(x-C)^2+Cx^2

圖片參考：http://imgcld.yimg.com/8/n/HA00133515/o/701010220120213873379350.jpg

Comparing the coefficient


圖片參考：http://imgcld.yimg.com/8/n/HA00133515/o/701010220120213873379361.jpg