Cannotta 3+3 Mathematics ?

1.
2m^2+3mn-2n^2-5m-10n
=(2m-n)(m+2n)-5(m+2n)
=(m+2n)(2m-n-5)

2.
A(2x+1)^2-3BX+(B-C) = (4x-1)(x-4)
A(4x^2+4x+1)-3Bx+B-C = 4x^2-x-16x+4
4Ax^2 +(4A-3B)x +(A+B-C) = 4x^2-17x+4
Comparing the coefficients of like terms,
A = 4
4A-3B=-17 => 16-3B=-17 => B=11
A+B-C=4 => 4+11-C=4 => C=11

3.
L.H.S.
=(n+1)^2-(n-2)^2
=n^2+2n+1-(n^2-4n+4)
=n^2+2n+1-n^2+4n-4
=6n-3
=3(2n-1)
=R.H.S.
Thus, it is an identity.

4.
L.H.S.
=(2a+b)^2-(a+2b)^2
=4a^2+4ab+b^2-(a^2+4ab+4b^2)
=4a^2+4ab+b^2-a^2-4ab-4b^2
=3a^2-3b^2
=3(a^2-b^2)
=3(a+b)(a-b)
=R.H.S.
Thus, it is an identity.