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# If (3x−2y)^2=ax^2+bxy+cy^2, what is the value of sum a+b+c?

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Re: If (3x−2y)^2=ax^2+bxy+cy^2, what is the value of sum a+b+c? [#permalink]
a = 9
b = -12
c = 4
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Re: If (3x−2y)^2=ax^2+bxy+cy^2, what is the value of sum a+b+c? [#permalink]
Bunuel wrote:
If $$(3x−2y)^2=ax^2+bxy+cy^2$$, what is the value of sum a+b+c?

A. -7
B. -1
C. 1
D. 5
E. 7

We can expand (3x - 2y)^2 and we have:

9x^2 - 12xy + 4y^2

Thus:

9x^2 - 12xy + 4y^2 = ax^2 + bxy + cy^2

Furthermore we can say:

9x^2 = ax^2, so a = 9

-12xy = bxy, so -12 = b

4y^2 = cy^2, so 4 = c

Thus, a + b + c = 9 - 12 + 4 = 1.