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lines changed Original file line number Diff line number Diff line change 11${(5x-36)}^{100}$
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3- $ = \sum^{100}_ {k=0} \binom{100}{k} {(5x)}^{n-k} {(-3y)}^{k} $
3+ $ = \sum^{100}\ _ {k=0} \binom{100}{k} {(5x)}^{n-k} {(-3y)}^{k} $
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55We only consider $k=80$, as it results in $y^{80}$.
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Original file line number Diff line number Diff line change 1- $ = \sum^{20}_ {k=0} \binom{20}{k} {(-3x)}^{n-k} {(5y)}^{k} $
1+ $ = \sum^{20}\ _ {k=0} \binom{20}{k} {(-3x)}^{n-k} {(5y)}^{k} $
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33We only consider $k=5$, as it results in $y^{5}$.
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Original file line number Diff line number Diff line change 11$ {(2x-7y)}^{15} $
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3- $ = \sum _ {k=0}^{15} \binom{15}{k} {(2x)}^{n-k} {(-7y)}^{k} $
3+ $ = \sum \_ {k=0}^{15} \binom{15}{k} {(2x)}^{n-k} {(-7y)}^{k} $
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55We only consider $k=11$, as it results in $y^{11}$.
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@@ -10,4 +10,4 @@ $ = \binom{15}{11} \cdot 2^{4} \cdot {(-7)}^{11} \cdot x^4 \cdot y^{11} $
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1111$ = - \binom{15}{4} \cdot 2^{4} \cdot 7^{11} \cdot x^4 \cdot y^{11} $
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13- Thus, the coefficient of $ x^{4}y^{11} $ in the expansion of $ {(2x-7y)}^{15} $ is $ - \binom{15}{11} \cdot {2}^{4} \cdot {7}^{11} $
13+ Thus, the coefficient of $ x^{4}y^{11} $ in the expansion of $ {(2x-7y)}^{15} $ is $ - \binom{15}{11} \cdot {2}^{4} \cdot {7}^{11} $
Original file line number Diff line number Diff line change 1- $ = \sum^{50}_ {k=0} \binom{50}{k} {(5x)}^{n-k} {(-7y)}^k $
1+ $ = \sum^{50}\ _ {k=0} \binom{50}{k} {(5x)}^{n-k} {(-7y)}^k $
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33We only consider $k=26$, as it results in $y^{26}$.
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@@ -8,4 +8,4 @@ $ = \binom{50}{26} \cdot {(5)}^{24} \cdot x^{24} \cdot {(-7)}^{26} \cdot y^{26}
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99$ = \binom{50}{26} \cdot 5^{24} \cdot 7^{26} \cdot x^{24} \cdot y^{26} $
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11- Thus, the coefficient is $ \binom{50}{26} \cdot 5^{24} \cdot 7^{26} $
11+ Thus, the coefficient is $ \binom{50}{26} \cdot 5^{24} \cdot 7^{26} $
Original file line number Diff line number Diff line change 1- $ = \sum^{100}_ {k=0} \binom{100}{k} {(7x)}^{n-k} {(-13y)}^{k} $
1+ $ = \sum^{100}\ _ {k=0} \binom{100}{k} {(7x)}^{n-k} {(-13y)}^{k} $
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33We only consider $k=80$, as it results in $y^{80}$.
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Original file line number Diff line number Diff line change 1- $ = \sum _ {k=0}^{55} \binom{55}{k} {(5x)}^{n-k} {(-3y)}^{k} $
1+ $ = \sum \_ {k=0}^{55} \binom{55}{k} {(5x)}^{n-k} {(-3y)}^{k} $
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33We only consider $k=35$, as it results in $y^{35}$.
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Original file line number Diff line number Diff line change 11$ (2x - 3y)^{30} $
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3- $ = \sum _ {k=0}^{30} \binom{30}{k} \cdot (2x)^{n-k} \cdot (-3y)^{k} $
3+ $ = \sum \_ {k=0}^{30} \binom{30}{k} \cdot (2x)^{n-k} \cdot (-3y)^{k} $
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55We only consider $k=20$, as it results in $y^{20}$.
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