Algebra - Binomische Formeln

Binomische Formeln

$\boxed{(a + b)^2 = a^2 + 2ab + b^2}$ ('Plus'- Formel)

'Plus'- Formel: $(a + b)^2 = (a + b)(a + b) = a^2 + ab + ba + b^2 = a^2 + ab + ab + b^2 = a^2 + 2ab + b^2$ q.e.d.

('Minus'- Formel) $(a - b)^2 = (a - b)(a - b) = a^2 - ab - ba + b^2 = a^2 - ab - ab + b^2 = a^2 - 2ab + b^2$ q.e.d.

$\boxed{(a - b)^2 = a^2 - 2ab + b^2}$ ('Minus'- Formel)

$\boxed{(a + b)(a - b) = a^2 - b^2}$ ('Plus-Minus'- Formel)

('Plus-Minus'- Formel) $(a + b)(a - b) = a^2 - ab + ba - b^2 = a^2 - ab + ab - b^2 = a^2 - b^2$ q.e.d.

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