**Question**

**Introduction**

We have
seen here, here and here
that recognising chunks is useful in mathematics. It is an example of a having what Carolyn Kieran
calls a structural view of algebra, which is a type of pattern recognition. In this article, I show how, using chunking
and substitution, we can piggy-back or ride on solutions of a simpler equation
to obtain solutions of a more complicated equation.

The solution
for part (a) of is easy enough. Just

**factorise**(or*Am*E. “factor”)
(

*y*+ 2)(*y*– 7) = 0
Hence

*y*+ 2 = 0 or*y*– 7 = 0*y*= -2 or

*y*= 7

This is Standard Operating Procedure. But part (b) seems like a monster of an
equation. Oh dear! What shall we do?

**Observation**

Can you observe anything appearing more
than once?

Now
do you notice any chunks that are repeated?
Once you can see the connection, you can make a substitution

*y*=*x*^{3}– 1 and then make use of the answer in part (a). We copy and paste the chunk (shown in green) into the previous solution and proceed from there.**Solution to part (b)**

*x*

^{3}– 1 = -2 or

*x*

^{3}– 1 = 7

*x*

^{3}= -1 or

*x*

^{3}= 8

*x*= -1 or

*x*= 2

Solved!

H04. Look for pattern(s)

H05. Work backwards

H09. Restate the problem in
another way

H11. Solve part of the problem

H13* Use Equation / write a
Mathematical Sentence

**Suitable Levels**

*****Lower Secondary Mathematics (Sec 2 ~ Grade 8-9)

*****any syllabus that includes algebraic factorisation (factoring) and substitution

*****anyone who is interested in and ready for algebra

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