document.write( "Question 935346: How do you: \r
\n" ); document.write( "\n" ); document.write( "Find the coefficient of x^4 in the binomial expansion of (5+2x)^7\r
\n" ); document.write( "\n" ); document.write( "(with steps please) \n" ); document.write( "
Algebra.Com's Answer #568587 by MathTherapy(10552)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "Find the coefficient of x^4 in the binomial expansion of (5+2x)^7
\n" ); document.write( "(with steps please)
\n" ); document.write( "
Formula for a specific term in an expansion: (a + b)n = nCr-1(a)n-(r-1)(b)r-1, where r = term number 
\n" );
document.write( "(5 + 2x)7
\n" );
document.write( "Observing the binomial, it’s seen that the x-term, or “b” in the expansion of the binomial needs to be to the 4th power. 
\n" );
document.write( "Thus, the term that produces \"b%5E4\" is the term that needs to be determined. Thus, we can say that: \"b%5E4+=+b%5E%28r+-+1%29\", and that: 
\n" );
document.write( "4 = r – 1
\n" );
document.write( "4 + 1 = r
\n" );
document.write( "r, or term number = 5\r
\n" );
document.write( "\n" );
document.write( "Using the formula for a specific term in an expansion, term 5 or the 5th term can be determined, as follows: 
\n" );
document.write( " (a + b)n = nCr-1(a)n-(r-1)(b)r-1, where r = term number 
\n" );
document.write( "(5 + 2x)7 = 7C5-1(5)7-(5-1)(2x)5-1, where r = 5th term 
\n" );
document.write( "(5 + 2x)7 = 7C4(5)7-4(2x)4
\n" );
document.write( "(5 + 2x)7 = 35(5)3(2x)4
\n" );
document.write( "(5 + 2x)7 = 4,375(16)x4
\n" );
document.write( "(5 + 2x)7 = 70,000x4
\n" );
document.write( "Thus, the \"x%5E4\" term, or 5th term of the binomial expansion: \"%285+%2B+2x%29%5E7\", is 70,000x4, which means
\n" );
document.write( "that the coefficient is \"highlight_green%28highlight_green%2870000%29%29\"\r
\n" );
document.write( "\n" );
document.write( "Not to be confused, if the binomial's expressions were rearranged from \"%285+%2B+2x%29%5E7\" to \"%282x+%2B+5%29%5E7\",
\n" );
document.write( "then \"a%5E4\" or \"%282x%29%5E4\" would be the 4th term.
\n" );
document.write( "You can do the check!! 
\n" );
document.write( "===================
\n" );
document.write( "Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com.
\n" );
document.write( "Further help is available, online or in-person, for a fee, obviously. \r
\n" );
document.write( "\n" );
document.write( "For FREE info and answers to questions about the ASVAB exam, the NYS 3 – 8 city/state wide exams,GENERAL
\n" );
document.write( "MATH and HOMEWORK QUESTIONS, or MATH QUESTIONS related to the Regents Integrated Algebra, 
\n" );
document.write( "Regents Geometry, Regents Algebra 2/Trigonometry, SHSAT, COOP/HSPT/TACHS, PSAT, SAT, ACT, SSAT/ISEE,
\n" );
document.write( "GRE, CLEP, and the TASC/GED, you can visit: http://asvabstudyzone.freeforums.net/. \n" );
document.write( "
\n" );