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What is the value for c that will make

9x2 + 12xy + c
a perfect square trinomial

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Shelly J. | Excellent Maths Tutoring for academic successExcellent Maths Tutoring for academic su...
5.0 5.0 (233 lesson ratings) (233)
4
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

Comments

Thank you Shelly.  I did not think of that possibility.
Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
-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
 

Comments

If there is a y, then I do not know how to resolve c such that this is a perfect square.