What is the value for c that will make

Question

9x² + 12xy + c

a perfect square trinomial

Answer 1

Hi Stacy,

 

(a+b)² = (a)²+2(a)(b)+(b)²

 

9x²+12xy+c = (3x)²+2(3x)(2y)+(2y)²

 

                   =(3x+2y)²

 

c=(2y)²=4y²

Answer 2

Hi Stacy;

9x² + 12xy + c

I think this is...

9x² + 12x + c........There is no y...

 

For the FOIL...

FIRST...(3x)(3x)=9x²

OUTER and INNER must add-up to 12x.  Because the coefficient of each x is 3, and because there are 2 parenthetical equations, and because the second number of the parenthetical equation must duplicate, we can calculate this second number of the parenthetical equations by (3)(2)(?)=12....?=2.

(3x+2)²
(3x+2)(3x+2)

Let's FOIL...

FIRST...(3x)(3x)=9x²

OUTER...(3x)(2)=6x

INNER...(2)(3x)=6x

LAST...(2)(2)=4

9x²+6x+6x+4

9x²+12x+4

c=4