> [!summary] An algebraic proof is a type of proof where you show that LHS = RHS using algebra and manipulation. >[!info]+ Read Time **⏱ 1 min** # Definition An algebraic proof is a type of proof that relies on algebraic identities and manipulation (factoring, simplifying, [[Greatest Common Divisor (gcd)|greatest common divisors]], etc)to show that expressions are equal (Left hand side = Right hand side). # Examples > [!example] Show that $(a+b)^2 = a^2 + 2ab + b^2$ > > $ \begin{align*} (a+b)^2 &= (a+b)(a+b) \\ &= a\cdot a +a\cdot b+b\cdot a + b\cdot b \\ &= a^2 + 2ab + b^2 \end{align*} > $ > Therefore, using algebraic proof, LS = RS > [!example] Prove algebraically that the sum of two consecutive integers is always odd. > > Let any integer be $n$ Two consecutive integers are $n + n+1$ The sum of these is $2n +1$ This is the identity of a [[Even & Odd Numbers|odd number]] --- > 📚 Like this note? [Star the GitHub repo](https://github.com/rajeevphysics/Obsidian-MathMatter) to support the project and help others discover it! ---