More examples of deductive proofs, tricks for proofs (using odd, even, consecutive integers)

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a) Show that $latex \left ( a+b \right )^{2}=a^{2}+2ab+b^{2}$.

b) Prove that the sum of six consecutive positive integers is a multiple of 3.

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Answer:a) Show the expansion: $latex \left ( a+b \right )^{2}=\left ( a+b \right )\left ( a+b \right )=a^{2}+ab+ab+b^{2}=a^{2}+2ab+b^{2}$. LHS = RHS.

b) Let x = positive integer. $latex \frac{6x+15}{3}=2x+5$, which shows that it is a multiple of 3.

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