document.write( "Question 986242: What is the coefficient of $\"x%5E3y%5E4\"$ in the binomial expansion of $\"%28x%2By%29%5E7\"$ ?\r
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Algebra.Com's Answer #607076 by MathTherapy(10552) $\"\"$ $\"About$

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What is the coefficient of $\"x%5E3y%5E4\"$ in the binomial expansion of $\"%28x%2By%29%5E7\"$ ?\r
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For this problem, the formula to determine a specific term in a Bernoulli/Binomial expansion should be used. It states:
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document.write( ", where r = term number \r
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document.write( "We have: , which becomes: 
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document.write( "The expression: , without its coefficient, occurs at the term where 
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document.write( "Thus, 3 = 7 - (r - 1)
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document.write( "3 = 7 - r + 1
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document.write( "3 = 8 - r
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document.write( "3 - 8 = - r 
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document.write( "- 5 = - r
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document.write( "r, or term number where  occurs = , or 5 \r
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document.write( "Confirming this, and as seen above,  occurs at , and so:
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document.write( "4 = r - 1
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document.write( "4 + 1 = r
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document.write( "r, or term number where  occurs = 5 \r
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document.write( "This means that the expression:  without its coefficient occurs at the 5th term\r
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document.write( "We now have: , with r or term number being 5
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document.write( "This becomes:  
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document.write( "As seen the coefficient of  in the expansion of:  is:  \n" );
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