document.write( "Question 386772: If a term in the explansion of (x+b)^8 is (-1701x^3)/(4096), assuming b is a constant, then the exact value of b is? \n" ); document.write( "

Algebra.Com's Answer #273414 by robertb(5830) $\"\"$ $\"About$

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The binomial theorem states that, the (r+1)st term in the expansion of $\"%28a+%2B+b%29%5En\"$ is $\"nCr%2Aa%5E%28n-r%29%2Ab%5Er\"$ . Applied directly to the problem at hand, knowing that the power of x should be 3, the term involving $\"x%5E3\"$ should then be $\"8C5%2Ax%5E3%2Ab%5E5\"$ . Thus
\n" ); document.write( " $\"8C5+%2A+b%5E5+=+-1701%2F4096\"$ , after equating coefficients. Then
\n" ); document.write( " $\"56b%5E5+=+-1701%2F4096\"$ , or
\n" ); document.write( " $\"b%5E5+=+-243%2F32768\"$ , or
\n" ); document.write( " $\"b+=+-3%2F8\"$ . \n" ); document.write( "

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