document.write( "Question 103883This question is from textbook Beginning Algebra
\n" ); document.write( ": Is (a+b)^3 ever equal to a^3+b^3? Explain. \n" ); document.write( "

Algebra.Com's Answer #75881 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let's work it out
\n" ); document.write( " $\"%28a%2Bb%29%5E3=%28a%2Bb%29%2A%28a%2Bb%29%5E2\"$
\n" ); document.write( " $\"%28a%2Bb%29%5E3=%28a%2Bb%29%2A%28a%5E2%2B2ab%2Bb%5E2%29\"$
\n" ); document.write( " $\"%28a%2Bb%29%5E3=a%2A%28a%5E2%2B2ab%2Bb%5E2%29%2Bb%2A%28a%5E2%2B2ab%2Bb%5E2%29\"$
\n" ); document.write( " $\"%28a%2Bb%29%5E3=%28a%5E3%2B2a%5E2b%2Bab%5E2%29%2B%28ba%5E2%2B2ab%5E2%2Bb%5E3%29\"$
\n" ); document.write( " $\"%28a%2Bb%29%5E3=a%5E3%2B3a%5E2b%2B3ab%5E2%2Bb%5E3\"$
\n" ); document.write( "Now let's substitute.
\n" ); document.write( " $\"%28a%2Bb%29%5E3=a%5E3%2Bb%5E3\"$ Your original equation.
\n" ); document.write( " $\"cross%28a%5E3%29%2B3a%5E2b%2B3ab%5E2%2Bcross%28b%5E3%29=cross%28a%5E3%29%2Bcross%28b%5E3%29\"$ Substitute for the expanded cubic amd remove like terms from both sides.\r
\n" ); document.write( "\n" ); document.write( " $\"3a%5E2b%2B3ab%5E2=0\"$ Simplify.
\n" ); document.write( " $\"%283a%5E2b%2B3ab%5E2%29%2F%283ab%29=0\"$ Divide both sides by 3ab
\n" ); document.write( " $\"%283a%5E2b%29%2F3ab%2B%283ab%5E2%29%2F3ab=0\"$ Distribute.
\n" ); document.write( " $\"a%2Bb=0\"$ Simplify
\n" ); document.write( "So whenever a+b=0, then you know that
\n" ); document.write( " $\"%28a%2Bb%29%5E3=a%5E3%2Bb%5E3\"$
\n" ); document.write( "For example,
\n" ); document.write( " $\"a=3\"$ and $\"b=-3\"$
\n" ); document.write( " $\"a%2Bb=0\"$ and $\"%28a%2Bb%29%5E3=0\"$
\n" ); document.write( " $\"a%5E3%2Bb%5E3=%2827%29%2B%28-27%29=0\"$ \n" ); document.write( "

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