Math

a2 – b2 = (a – b)(a + b) (a + b)2 = a2 + 2ab + b2 a2 + b2 = (a + b)2 – 2ab. (a – b)2 = a2 – 2ab + b2 (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca. (a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca. (a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b) If n is a natural number an – bn = (a – b)(an-1 + an-2b+…+ bn-2a + bn-1) If n is even (n = 2k), an + bn = (a + b)(an-1 – an-2b +…+ bn-2a – bn-1) If n is odd (n = 2k + 1), an + bn = (a + b)(an-1 – an-2b +an-3b2…- bn-2a + bn-1) (a + b + c + …)2 = a2 + b2 + c2 + … + 2(ab + ac + bc + ….) aaaaaa Roots of Quadratic Equation For a quadratic equation ax2 + bx + c = 0 where a ≠ 0, the roots will be given by the equation as Δ = b2 − 4ac is called the discriminant For real and distinct roots, Δ > 0 For real and coincident roots, Δ = 0 For non-real roots, Δ < 0 If α and β are the two roots of the equation ax2 + bx + c = 0 then, α + β = (-b / a) and α × β = (c / a). If the roots of a quadratic equation are α and β, the equation will be (x − α)(x − β) = 0 [outro] [end]