Which value of b would make #16x^2 -bx+25# a perfect square trinomial?

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Answer 1 · 2017-01-11T04:39:21

b = 40 and -40

General form of Perfect square trinomial is #a^2+2ab+b^2#

Therefore from
#16x^2-bx+25#

#a^2=sqrt(16x^2), b^2=25#, then

#a = +-4x, b=+-5#

take consideration a=4x and b=-5 (different sign), then
#-bx = 2(4x)(-5)#
#-bx = -40x#
#b=40#
The perfect square is #(4x-5)^2 = 16x^2-40x+25#.

if we consider a=4x and b=5 (same sign), then
#-bx = 2(4x)(5)#
#-bx = 40x#
#b=-40#
The perfect square is #(4x+5)^2=16x^2+40x+25#.

The first solution #(4x-5)^2# is the best solution after comparing the expression given.