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

1 Answer
Jan 11, 2017

b = 40 and -40

Explanation:

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.