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3 Quadratic Formula Finally, the quadratic formula if a, b and c are real numbers, then the quadratic polynomial equation ax2 bx c = 0 (31) has (either one or two) solutions x = b p b2 4ac 2a (32) 4 Points and Lines Given two points in the plane, P = (x 1;y 1);$$(a b c)^3 = (a^3 b^3 c^3) (3a^2b 3a^2c 3abc) (3ab^2 3b^2c 3abc) (3ac^2 3bc^2 3abc) 3abc$$ $$(a b c)^3 = (a^3 b^3 c^3) 3a(ab ac bc) 3b(ab bc ac) 3c(ac bc ab) 3abc$$There are n 4 – 1 C 4 – 1 = n 3 C 3 terms in the above expansion REMARK The greatest coefficient in the expansion of (x 1 x 2 x m ) n is (n!) / (q!) m – r {(q1)!} r , where q and r are the quotient and remainder, respectively when n is divided by m Example 14 Prove That B C A A B C A B C C A B 4abc (a+b+c)^3 formula expansion