Discrete math

Prove the following identities for p, q, m, nz, and y real numbers: Let P and q be two real numbers, and let LHS = 8(p-q) +4(p+q) and RHS = 2(p+3g)+ 10p-). Then: 12p-49 = and 12p-49 = Therefore LHS RHS for all p and g, and the identity is true Let z, y, m and n be four real numbers, and let LHS m(z y) +ny-z). Then z(m-n) + y(n + m) and RHS = and RHS-m+y Therefore L.HS -RHS for all , y, n and m, and the identity is true. c) (z+3)(z +8) _ (z-6)(1-4) = 211 Letr be a real number and let LIIS-(z + 3)(z + 8)-(z-6)(1-4) and RHS = 21z. Then: LHS2+83+24-+6 24 = 21 = RHS The identity is true for all Let m be a real number and let LHS = ms _ 1 and RHS = (m2-1)(+1)(m" + 1, Then LHS (m")2-12 = ((m2)2-1)(m4 + 1) = RHS The identity is true for all