F2 Maths... about identities... 快入``

1)

Expand it and get Ax^2 + Bx + (B - C) ≡ -x^2 - 6x +12
Compare like terms and get A = -1, B = -6, B - C = 12
=> A = -1, B = -6, C = -18

2)

Expand and get Bx^2 + (AB - 1)x - A ≡ 2x^2 + Cx - 2
Compare like terms and get B = 2, AB - 1 = C, -A = -2
=> A = 2, B = 2, C = 3

1 )
Ax^2+B(x+1)-C≡6(x+2)-x(x+12)
LHS = Ax^2+B(x+1)-C
= Ax^2+BX+B-C

RHS = 6(x+2)-x(x+12)
= 6x+12-x^2+12x
= 6x+12x+12-x^2
= 18x+12-2x^2
= -x^2+18x+12

Because Ax^2+BX+B-C ≡ 18x+12-x^2
Therefore
Ax^2 = - x^2
A = - 1
B = 18
C = -12


2 )
(x+A)(Bx-1)≡2(x^2-1)+Cx
LHS = (x+A)(Bx-1)
= (x)(Bx-1)+(A)(Bx-1)
= (x)(Bx)-(x)(1)+(A)(Bx)-(A)(1)
= Bx^2 - x - ABx - A
= Bx^2 - A - ABx - x

RHS = 2(x^2-1)+Cx
= 2x^2-2+Cx

Because Bx^2 - A - ABx - x ≡ 2x^2-2+Cx
Therefore
B = 2
A = -2
C = -ABx
C = -(-2)2
C = 4