**Question**

**Introduction**

This lower
secondary algebra question seems complicated, doesn’t it? Can you spot any chunk that is repeated, or
almost the same? This is one of the keys
to solving the problem. Another key that
you need is the relevant algebraic identities and tricks.

**Reminders**

First, let
us review some of these useful formulas.

This is the square-of-difference identity, illustrated here.

Looking
back at the question, do you notice anything that is repeated? Can you see any chunks that are the same or
almost the same? (

*n*– 2011) is almost the same as (2012 –*n*) isn’t it? Whenever you see a repeated chunk, it is a good idea to substitute that chunk with another variable that you invent. To name this new variable, you can use any letter that is not used before, so as not to conflict with existing letter(s).**Solution**

**Summary**

To solve
the given problem, we have used the following:-

(1) square-of-difference identity

(2) swapping technique

(3) observation of repeated chunks

(4) using substitution with the chunks

H04. Look for
pattern(s) e.g. chunking, observation

H09. Restate
the problem in another way e.g.
swapping, identities

H10. Simplify
the problem e.g. substitution for chunks

H11. Solve part
of the problem

H12* Think of a
related problem

H13* Use
Equation / write a Mathematical Sentence

**Suitable Levels**

**·**

**Lower Secondary Mathematics**

**·**other syllabuses that involve whole numbers and ratios

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