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Sub 505 Level|   Algebra|      
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Bunuel
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If (3x−2y)^2=ax^2+bxy+cy^2, what is the value of sum a+b+c? 02 Mar 2017, 08:11
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C
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5% (low)

Question Stats:

85% (01:02) correct 15% (01:25) wrong based on 93 sessions

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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
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C
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If (3x−2y)^2=ax^2+bxy+cy^2, what is the value of sum a+b+c? 02 Mar 2017, 08:35
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(3x−2y) ²
(3x - 2y)(2x - 2y)
3x(3x - 2y) - 2y (3x - 2y)
9x² - 6xy - 6xy + 4y²
9x² - 12xy + 4y²

therefore a + b + c = 9 + -12 + 4 = 1.
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If (3x−2y)^2=ax^2+bxy+cy^2, what is the value of sum a+b+c? 02 Mar 2017, 09:08
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Expanding the quadratic : \((3x−2y)^2\) = 9x^2 - 12xy + 4y^2

Equating LHH to RHS
a = 9, b = -12, c = 4

a+b+c = 9 - 12 + 4 = 1
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If (3x−2y)^2=ax^2+bxy+cy^2, what is the value of sum a+b+c? 02 Mar 2017, 10:33
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Answer c
a = 9
b = -12
c = 4
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If (3x−2y)^2=ax^2+bxy+cy^2, what is the value of sum a+b+c? 07 Mar 2017, 07:41
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Bunuel
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.

Answer: C
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