Question

10 formule matematice
Exemple plus rezolvările

Answer 1

Formula 1

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

Demonstratie :

${(a - b)}^{2} = (a - b) \times (a - b) = a \times a + a \times ( - b) + ( - b) \times a + ( - b) \times ( - b) = {a }^{2} - ab - ba + {b}^{2} = {a}^{2} + {b}^{2} - 2ab$

Exemplu:

${(5 - 3)}^{2} = {5}^{2} + {3}^{2} - 2 \times 5 \times 3 = 25 + 9 - 30 = 4$

Formula 2:

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

Demonstratie:

${(a + b)}^{2} = (a + b) \times (a + b) = a \times a + a \times b + b \times a + b \times b = {a}^{2} + {b}^{2} + 2ab$

Exemplu:

${(3 + 6)}^{2} = {3}^{2} + {6}^{2} + 2 \times 3 \times 6 = 9 + 36 + 36 = 81$

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