How do you simplify #(4p^2q + 5p^3q^2 - 6pq) - ( -2p^3q^2 + 5pq - 8p^2q)#?

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Answer 1 · 2016-04-11T09:28:32

#" "7p^3q^2+12p^2q-11pq#

Basically this is an exercise for keeping track.

Example: Suppose we had #-(6a-4b)#

This can be written as:#" "(-1)xx(6a-4b)#

Multiply everything inside the brackets by #(-1)# giving:
#-6a+4b#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Applying the same principle

Consider the right hand side expression:

We have: #(-1)xx(-2p^3q^2+5pq-8p^2q)#

#=>+2p^3q^2-5pq+8p^2q#

Putting it all together

#" "4p^2q+5p^3q^2-6pq+2p^3q^2-5pq+8p^2q#

Grouping terms

#" "(4p^2q+8p^2q)+(5p^3q^2+2p^3q^2)+(-6pq-5pq)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Think of #+# as 'put with'. That way we can write

#+(-6pq-5pq)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#" "12p^2q+7p^3q^2-11pq#

Changing the order based on #p#

#" "7p^3q^2+12p^2q-11pq#