Formule de calcul prescurtat

📐 Formule

Formule

${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$

${(a - b)}^{2} = a^{2} - 2 a b + b^{2}$

${(a + b + c)}^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 a c + 2 b c$

${(a - b + c)}^{2} = a^{2} + b^{2} {+ c}^{2} - 2 a b + 2 a c - 2 b c$

$a^{2} - b^{2} = (a - b) (a + b)$

${(a + b)}^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} = a^{3} + b^{3} + 3 a b (a + b)$

${(a - b)}^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}$

$a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$

$a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$

$a^{4} - b^{4} = (a - b) (a + b) (a^{2} + b^{2})$

💡 Exemple

${(4 + 5)}^{2} = 4^{2} + 2 * 4 * 5 + 5^{2} = 16 + 40 + 25 = 81$

Verificare: ${(4 + 5)}^{2} = 9^{2} = 81$

$102^{2} = {(100 + 2)}^{2} = 100^{2} + 2 \cdot 100 \cdot 2 + 4 = 10000 + 400 + 4 = 10404$