How do you factor #16y^2-4y-2#?

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Answer 1 · 2015-12-12T06:31:51

#color(blue)((8y+2)(2y-1) # is the factorised form of the expression.

#16y^2-4y-2#.

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*-2 = -32#

AND

#N_1 +N_2 = b = -4#

After trying out a few numbers we get #N_1 = -8# and #N_2 =4#
#4*-8 = -32#, and #4+(-8)= -4#

#16y^2color(blue)(-4y)-2 = 16y^2color(blue)(-8y +4y)-2#

#=8y(2y-1) +2(2y-1)#

#=color(blue)((8y+2)(2y-1) #