## Related questions with answers

Make a conjecture about each value or geometric relationship. the product of two odd numbers

Solutions

Verified3*3=9,
7*5=35,
9*1=9,
11*9=99

The product of two odd numbers will be an odd number.

Let $a$ and $b$ be any integers so that $(2a+1)$ and $(2b+1)$ are$\textbf{ two odd numbers}$.

Now, let's find its $\textbf{product}$:

$\begin{align*} (2a+1)\cdot (2b+1)&=4ab+2a+2b+1\\ &=\colorbox{Dandelion}{$2\cdot(2ab+a+b)+1$} \end{align*}$

Therefore, we can conclude that $\textbf{product of two odd numbers will also be odd}$.

A $\textbf{few examples}$ to support our reasoning:

$\begin{align*} 3 \cdot 9=27\quad&\Rightarrow\quad 27 =(13\cdot 2)+1 \quad\textcolor{#c34632}{\checkmark}\\ 21 \cdot 7=32\quad&\Rightarrow\quad 147 =(73\cdot 2)+1 \quad\textcolor{#c34632}{\checkmark}\\ 113 \cdot 5=180\quad&\Rightarrow\quad 565 =(282\cdot 2)+1 \quad\textcolor{#c34632}{\checkmark}\\ 19 \cdot 81=1008\quad&\Rightarrow\quad 1539 =(769\cdot 2)+1 \quad\textcolor{#c34632}{\checkmark}\\ 99 \cdot 11=4392\quad&\Rightarrow\quad 1089 =(544\cdot 2)+1\quad\textcolor{#c34632}{\checkmark}\\ \end{align*}$

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