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Q
uantitative
R
easoning &
P
roblem
S
olving
36
© 2014 Pacific Crest
The Practice
4. Analyze an Example
to tap into the expert’s thinking
Description
When/How
to Apply
Once you have the basics, 1) Find 2 or 3 examples 2) Follow the thinking 3) Compare & contrast
The examples used in class, in a textbook, or an explanation by a friend will most likely contain several
steps. They are broken into steps so you can follow the process used. Following the steps and their
explanation, to the degree that you can then explain it to someone else effectively turns you into an
expert as well. Or at least someone who has learned to apply expert-level thinking in the context of the
example.
Examples
Pick a number other than 0, 1, and –1
to substitute for the variable in both the
original and simplified expressions. If
both values are equivalent, you have
validated your work.
Distribute through the expression so as to
remove all parentheses within the expression.
Check signs, reviewing all coefficients for accuracy in signs,
carefully checking for negatives and double negatives.
Look through every term to inventory how many like terms
you will have and produce that number of groupings.
Set up the buckets with the variables from the previous step using
parentheses and addition signs. Rearrange the original expression
by grouping coefficients within the appropriate parentheses.
Make sure that all terms in the previous expression
are accounted for by lightly crossing out, term by
term, each term that has been incorporated.
Convention says that each variable has a single
coefficient and that the computations needed to
remove parentheses should be carried out.
2
2
2
2
2
: 2( 4) 3 ( 4)
2 8 3
4
2 ,
3
8, 4
( )
( ) ( )
( 3 ) (2 ) ( 8 4)
2
simplify x
x x
x
x x
x x
x
x
x
x
x x
x
− − − −
− − − +
−
−
−
+
+
− + − + − +
2
8 3
x
− −
x
−
4
+
2
( 3
x
−
) ( 2
x
+
x
−
) ( 8
+ −
4
+
2
2
2
2
2
2
2
)
3 (2 ) ( 8 4)
3 ( ) ( 4)
3
4
Let
2
2( 4) 3 ( 4)
3
4
2(2 4) 3(2) (2 4)
3(2) 2 4
2( 2) 3(4) 2
3(4) 2
4 12 2 14
12 2 14
x
x x
x x
x x
x
x
x x
x x
− + − + − +
− + + −
− + −
=
− − − −
− + −
− − − −
− + −
− − +
− −
− − + = −
− − = −