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The expansion of (203x^2 - 199x - 3)(72y^2 + 27y + 1)

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The expansion of (203x^2 - 199x - 3)(72y^2 + 27y + 1)  [#permalink]

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New post 27 Nov 2019, 04:31
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[GMAT math practice question]

The expansion of \((203x^2 - 199x - 3)(72y^2 + 27y + 1)\) is a1x^2y^2 + a2x^2y + a3x^2 +…..+ a7y^2 + a8y + a9. What is a1 + a2 + a3 +…..+ a7 + a8 + a9?

A. \(100\)

B. \(122\)

C. \(125\)

D. \(200\)

E. \(228\)

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Re: The expansion of (203x^2 - 199x - 3)(72y^2 + 27y + 1)  [#permalink]

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New post 27 Nov 2019, 13:09
\((203x^2 - 199x - 3)(72y^2 + 27y + 1)\) = a1x^2y^2 + a2x^2y + a3x^2 +…..+ a7y^2 + a8y + a9

Put x=1 and y=1

(203-199-3)(72+27+1)=\( a1 + a2 + a3 +…..+ a7 + a8 + a9\)

1*100= \(a1 + a2 + a3 +…..+ a7 + a8 + a9\)

100= \(a1 + a2 + a3 +…..+ a7 + a8 + a9\)


MathRevolution wrote:
[GMAT math practice question]

The expansion of \((203x^2 - 199x - 3)(72y^2 + 27y + 1)\) is a1x^2y^2 + a2x^2y + a3x^2 +…..+ a7y^2 + a8y + a9. What is a1 + a2 + a3 +…..+ a7 + a8 + a9?

A. \(100\)

B. \(122\)

C. \(125\)

D. \(200\)

E. \(228\)
Math Revolution GMAT Instructor
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V
Joined: 16 Aug 2015
Posts: 8251
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The expansion of (203x^2 - 199x - 3)(72y^2 + 27y + 1)  [#permalink]

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New post 29 Nov 2019, 01:40
=>

When we substitute x and y with \(1’s\),
we have a1 + a2 + a3 +…..+ a7 + a8 + a9
= a1\((1)^2(1)^2\) + a2\((1)^2(1)\) + a3\((1)^2\) +…..+ a7\((1)^2\) + a8\((1)\) + a9.

\(= (203(1)^2 - 199(1) - 3)(72(1)^2 + 27(1) + 1)\)

\(= 1*100\)

\(= 100\)

Therefore, A is the answer.
Answer: A
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Re: The expansion of (203x^2 - 199x - 3)(72y^2 + 27y + 1)   [#permalink] 29 Nov 2019, 01:40
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