9x2+bx+16 whats b so its a perfect sqaure

Question

What is the value of b

Answer 1

Remember F-O-I-L

    (x+a)(x+b) = x² + bx + ax + ab  = x² + (a+b)x + ab

 

For a perfect square:

    (x+y)(x+y) = x² + 2yx + y²

 

 9x² + bx + 16  =  (3x+4) = 9x² + 8x + 16

     So, b=8        [note: for (x+y)², b = 2y and, given ax² + bx + c, y=SQRT(c), so, b=2*SQRT(c)