document.write( "Question 278641: (x+3)^3 \n" ); document.write( "

Algebra.Com's Answer #202743 by Alan3354(69443) $\"\"$ $\"About$

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(x+3)^3
\n" ); document.write( "--------
\n" ); document.write( "= $\"x%5E3+%2B+9x%5E2+%2B+27x+%2B+27\"$
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\n" ); document.write( "It is NOT x^3 + 27
\n" ); document.write( "To prove that x^3 + 27 is not right:
\n" ); document.write( "Let x = 1
\n" ); document.write( "(1 + 3)^3 = 64
\n" ); document.write( "1^3 + 3^3 = 28
\n" ); document.write( "Not equal. It has to be equal for all values of x
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\n" ); document.write( "You can multiply it out a step at a time:
\n" ); document.write( "= (x+3)*(x+3)*(x+3)
\n" ); document.write( "= (x+3)*(x^2 + 6x + 9)
\n" ); document.write( "= as above
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\n" ); document.write( "Or use Pascal's triangle:
\n" ); document.write( "1
\n" ); document.write( "1 2 1
\n" ); document.write( "1 3 3 1
\n" ); document.write( "(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 (using the 1 3 3 1 coefficients)
\n" ); document.write( "a = x, b = 3
\n" ); document.write( "--> as above
\n" ); document.write( " \n" ); document.write( "

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