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The ways to complete the first one is to realise that it involves a difference of two squares. If you were to see (X^2) with a constant (number), you know they have no factor in common, meaning the two te...

Mn²⁺ + 4H₂O => MnO^{​​​​​}₄^- + 8H⁺  + 5e^-

The proton's relative charge is +1 The neutron's relative charge is 0 The electron's relative charge is -1.

x = (-2 +/- sqrt(4-8))/2                    therefore x = - 1 +/- i, where i is the imaginary unit

y² + 2xy dy/dx = 3cos(3x) + 1/y - x/y² dy/dx                   thereforedy/dx = (3cos(3x) + 1/y - y²​​​​​​) / (2xy + x/y²)