ThmDex – An index of mathematical definitions, results, and conjectures.
Result R5172 on D2167: Binomial coefficient
Real binomial theorem for exponent seven
Formulation 0
Let $a, b \in \mathbb{R}$ each be a D993: Real number.
Then \begin{equation} \begin{split} (a + b)^7 = a^7 + 7 a^6 b + 21 a^5 b^2 + 35 a^4 b^3 + 35 a^3 b^4 + 21 a^2 b^5 + 7 a b^6 + b^7 \end{split} \end{equation}
Proofs
Proof 0
Let $a, b \in \mathbb{R}$ each be a D993: Real number.
This result is a particular case of R2788: Real binomial theorem. $\square$