Question 75063
I don't quite understand your question but I think you're asking..."How would I factor this trinomial" Am I right?
Factor:
{{{16x^2+40xy+25y^2}}} Notice that the first and last terms are perfect squares.
{{{(4x)^2 + 40xy + (5y)^2}}} This suggests the possibility that the factors might be squared.  Let's see!
{{{(4x)^2+40xy+(5y)^2 = (4x+5y)(4x+5y)}}}
To check this, we'll multiply theses factors to see if we get back the original trinomial: Using the FOIL method...
{{{(4x+5y)(4x+5y) = 16x^2+ 20xy+20xy+25y^2}}} Simplify this to get {{{16x^2+40xy+25y^2}}} and this is your original trinomial.
So the factors are: {{{(4x+5y)(4x+5y) = (4x+5y)^2}}}