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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)

by Max@Math Revolution » Wed Nov 27, 2019 3:06 am
[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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by Max@Math Revolution » Fri Nov 29, 2019 12:15 am
=>

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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