Step by step
The question
Question: prove that the product of two even numbers is even.
1 Write it with letters
x is even, so x = 2a, where a is a whole number.
That is what even means.
y is even, so y = 2b, where b is a whole number.
A new letter, b: y can be a different number from x.
Careful!
The same letter would make x and y the same number.
Two numbers need two letters.
2 Put them in
Now put them in: xy becomes (2a)(2b).
3 Work it out
Every part times every part: 4ab.
4 Show the form
Every term has a 2 in it.
We take out 2: 2 × 2ab.
2ab is a whole number, because whole numbers added and multiplied stay whole.
2 times a whole number: so xy is even.
The square at the end means: the proof is done.
5 Check
An example: x = 2 and y = 4.
It gives 8.
8 is 2 times 4: even, as the proof says.
Right!
Let's look back.
First: write it with letters.
Then: put them in.
Then: work it out.
Then: show the form.
Last: check.