How do you factor the trinomial #16y²+8y+1#?

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Answer 1 · 2016-03-16T12:32:59

# color(blue)((4y +1) (4y +1 ) # is the factorised form of the expression.

#16y^2 + 8y +1#

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like #ay^2 + by + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 16*1 =16#

and

#N_1 +N_2 = b = 8#

After trying out a few numbers we get #N_1 = 4# and #N_2 =4#

#4*4 = 16#, and #4+4= 8#

#16y^2 +color(green)( 8y) +1 =16y^2 +color(green)( 4y +4y )+1 #

#=4y (4y +1 ) + 1 (4y +1)#

#= color(blue)((4y +1) (4y +1 ) #

#color(blue)((4y +1) (4y +1 ) # is the factorised form of the expression.