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#MAASL00106/#MAAHL00028

Set r=3.

{_nC_3}\times(4x)^3\times(1)^{n-3}=320nx^3

Ignore 1^(n-3); cancel x^3.

64\times{_nC_3}=320n

{_nC_3}=5n

\frac{n!}{{3!\times(n-3)!}}=5n

\frac{{n\times(n-1)\times(n-2)\times(n-3)}}{{3!\times(n-3)!}}=5n

Cancel (n-3).

\frac{{n\times(n-1)\times(n-2)}}{6}=5n

\frac{{(n^2-n)\times(n-2)}}{6}=5n

n^3-3n^2+2n=30n

n^3-3n^2-28n=0

Factor to solve.

n(n+4)(n-7)=0

Check answers.

n=7

Explanation

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