中二簡單數學identities and factorize

1.If-(x-2)(3-x)=x^2+Bx+C.find the values of B and C
L.H.S. = -(x-2)(3-x)
= (x-2)(x-3)
= x^2 - 2x - 3x + 6
= x^2 - 5x + 6
By comparing the like terms on L.H.S. & R.H.S.,
B = -5, C = 6
2.Expand(mn+7)^2
(mn)^2 + 2(mn)(7) + 7^2
=(mn)^2 + 14mn + 49
3.factorize p^2r + pr- q^2r -qr
p^2r + pr- q^2r - qr
= r (p^2 - q^2 + p - q)
= r [(p+q)(p-q) + (p-q)]
= r(p-q)(p+q+1)
4.factorize 25h^2-(h^2+8h+16)
25h^2-(h^2+8h+16)
=(5h)^2 - [h^2 + 2(h)(4) + 4^2]
=(5h)^2 - (h+4)^2
=[5h + (h+4)] [5h - (h-4)]
=(6h + 4)(4h + 4)
=2(3h+2) * 4(h+1)
=8(3h+2)(h+1)