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 $p$

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

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