Step by step
The question
Question: prove that the sum of two consecutive odd numbers is a multiple of 4.
1 Write it with letters
Call the first number 2a + 1: an odd number, where a is a whole number.
The next odd numbers are 2 more each time: 2a + 1 + 2.
Careful!
An example shows one number.
The letters show every number at once.
2 Put them in
Add them up.
3 Work it out
Open the brackets: 2a + 1 + 2a + 1 + 2.
Like terms together: 4a + 4.
4 Show the form
Every term has a 4 in it.
We take out 4: 4(a + 1).
a + 1 is a whole number, because whole numbers added and multiplied stay whole.
4 times a whole number: so the sum is a multiple of 4.
The square at the end means: the proof is done.
5 Check
An example: 3, 5.
It gives 8.
8 is 4 times 2: a multiple of 4, 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.