Formule de calcul prescurtat

Asteptati un moment. Formulele se incarca...

$$ 1.\hspace{3pt} (a \pm b)^2 = a^2 \pm 2ab + b^2 $$ $$ 2.\hspace{3pt} a^2 - b^2 = (a - b)(a + b) $$ $$ 3.\hspace{3pt} (a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + ac + bc) $$ $$ 4.\hspace{3pt} (a \pm b)^3 = a^3 \pm 3a^2b + 3ab^2 \pm b^3 $$ $$ 5.\hspace{3pt} a^3 + b^3 = (a + b)(a^2 - ab + b^2) $$ $$ 6.\hspace{3pt} a^3 - b^3 = (a - b)(a^2 + ab + b^2) $$ $$ 7.\hspace{3pt} (a + b + c)^3 = a^3 + b^3 + c^3 + 3(a + b)(a + c)(b + c) $$ $$ \underline{Formule\hspace{3pt} generalizate:} $$ $$ 1.\hspace{3pt} a^n - b^n = (a - b)(a^{n-1}b^0 + a^{n-2}b^1 + ... + a^0b^{n-1}) $$ $$ 2.\hspace{3pt} a^{2n+1} + b^{2n+1} = (a + b)(a^{2n}b^0 - a^{2n-1}b^1 + ... - a^1b^{2n-1} + a^0b^{2n}) $$ $$ 3.\hspace{3pt} a^{2n} - b^{2n} = (a^2 - b^2)(a^{2n-2}b^0 + a^{2n-4}b^2 + ... + a^2b^{2n-4} + a^0b^{2n-2}) $$