How do you factor the trinomial a^2+6ab+9b^2?

Question

2692 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-30T00:23:42

The factored trinomial expression is #(a+3b)^2#.

Treat the trinomial like a quadratic expression.

Find two numbers that multiply to #9# and add up to #6#. These two numbers are #3# and #3#.

Now, split the middle term up into these terms, factor the first and last two terms separately, then combine them. The process looks like this:

#color(white)=a^2+6ab+9b^2#

#=a^2+3ab+3ab+9b^2#

#=color(red)a(a+3b)+3ab+9b^2#

#=color(red)a(a+3b)+color(blue)(3b)(a+3b)#

#=(color(red)a+color(blue)(3b))(a+3b)#

#=(a+3b)^2#

That's the factored trinomial. Hope this helped!