TITLE: Factoring with the grouping method
QUESTION [1 upvotes]: I'm trying to factor out using the grouping method the following polynomial:
$$
a(a+6)-(a+6)+a(a-4)-(a-4).
$$
The solution on the book is $2(x+1)(x-1)$.
Can someone explain the solution to me?

REPLY [0 votes]: You see a sum of four terms; two terms contain a factor $(a+6)$ ad two terms contain a factor $(a-4)$. We can group those two pairs as follows:
$$a(a+6)-(a+6)+a(a-4)-(a-4)=(a-1)(a+6)+(a-1)(a-4).$$
Now we have a sum of two terms, and both contain a factor $(a-1)$. We can group them as follows:
$$(a-1)(a+6)+(a-1)(a-4)=(a-1)(a+6+a-4)=(a-1)(2a+2).$$
This last factor can be written as $2a+2=2(a+1)$, and so rearranging the factors a bit we get
$$(a-1)(2a+2)=2(a-1)(a+1).$$
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