You can
put this solution on YOUR website! 9x² + 6x + 1
Multiply the 9 by the 1
You get 9
Think of two positive integers whose product is 9
and whose sum is 6.
That's easy! 3 times 3 is 9, and 3 plus 3 is 6.
So let's use 3 and 3 to rewrite the middle term 6x.
6x can be written as 3x + 3x.
So we rewrite
9x² + 6x + 1
as
9x² + 3x + 3x + 1
Factor 3x out of the first two terms
3x(3x + 1) + 3x + 1
Now put parentheses around the last two terms:
3x(3x + 1) + (3x + 1)
Put a 1 in front of that second parentheses:
3x(3x + 1) + 1(3x + 1)
I'll do some more coloring:
3x(3x + 1) + 1(3x + 1)
Factor out the red (3x + 1)
It leaves " 3x " from the first term and " + 1 " from
the second term. So we have
(3x + 1)(3x + 1)
Write that as a square:
(3x + 1)²
Edwin
