document.write( "Question 823878: I need more detail solution:
\n" ); document.write( "Evaluate A = (a^2 − 3a +1)^2 − (1− a)(−2a +1)(1− 3a) \n" ); document.write( "

Algebra.Com's Answer #496017 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
A way I think is easier:
\n" ); document.write( " $\"A=%28a%5E2-3a%2B1%29%5E2-%281-a%29%281-2a%29%281-3a%29\"$
\n" ); document.write( " $\"A=%28a%5E2%2B%281-3a%29%29%5E2-%281-3a%2B2a%5E2%29%281-3a%29\"$
\n" ); document.write( " $\"A=a%5E4%2B2a%5E2%281-3a%29%2B%281-3a%29%5E2-%281-3a%2B2a%5E2%29%281-3a%29\"$
\n" ); document.write( "Taking $\"%281-3a%29\"$ out as a common factor from $\"2a%5E2%281-3a%29\"$ and $\"%281-3a%29%5E2\"$ we get
\n" ); document.write( " $\"A=a%5E4%2B%281-3a%29%282a%5E2%2B1-3a%29%5E2-%281-3a%2B2a%5E2%29%281-3a%29\"$
\n" ); document.write( "Notice that the second term, $\"%281-3a%29%282a%5E2%2B1-3a%29%5E2\"$ ,
\n" ); document.write( "and the third term, $\"-%281-3a%2B2a%5E2%29%281-3a%29\"$ ,
\n" ); document.write( "are opposites and cancel each other out.
\n" ); document.write( "So we are left with
\n" ); document.write( " $\"A=a%5E4\"$
\n" ); document.write( "
\n" ); document.write( "The clench your teeth and dive in way:
\n" ); document.write( " $\"A=%28a%5E2-3a%2B1%29%5E2-%281-a%29%281-2a%29%281-3a%29\"$
\n" ); document.write( " $\"A=a%5E4-6a%5E3%2B11a%5E2-6a%2B1-%281-3a%2B2a%5E2%29%281-3a%29\"$
\n" ); document.write( " $\"A=a%5E4-6a%5E3%2B11a%5E2-6a%2B1-%281-6a%2B11a%5E2-6a%5E2%29\"$
\n" ); document.write( " $\"A=a%5E4%2B%28-6a%5E3%2B11a%5E2-6a%2B1%29-%281-6a%2B11a%5E2-6a%5E2%29\"$
\n" ); document.write( "Since the two expressions in brackets are the same, they cancel out, and we are left with
\n" ); document.write( " $\"A=a%5E4\"$
\n" ); document.write( "
\n" ); document.write( "TIP:
\n" ); document.write( "To calculate products like
\n" ); document.write( " $\"%28a%5E2-3a%2B1%29%5E2=%28a%5E2-3a%2B1%29%28a%5E2-3a%2B1%29=a%5E4-6a%5E3%2B11a%5E2-6a%2B1\"$ ,
\n" ); document.write( "it is better to calculate with pen and paper
\n" ); document.write( "by multiplying each term of $\"a%5E2-3a%2B1\"$ times $\"a%5E2-3a%2B1\"$ ,
\n" ); document.write( "writing each product in a row,
\n" ); document.write( "lining up like terms from the different products,
\n" ); document.write( "and then adding up the lines, like this:
\n" ); document.write( "

\n" ); document.write( "------------------------------
\n" ); document.write( " $\"matrix%281%2C7%2Ca%5E4%2C-6a%5E3%2C%22%2B%22%2Ca%5E2%2C-61%2C%22%2B%22%2C1%29\"$ $\"matrix%281%2C2%2C%22=%22%2C%28a%5E2-3a%2B1%29%28a%5E2-3a%2B1%29%29\"$
\n" ); document.write( "I do it that way, writing only the parts on the left, before the = sign (the rest I only wrote it here to describe how I calculated each line).
\n" ); document.write( "Trying to write the calculations on one line, I would get confused and make a mistake. \n" ); document.write( "

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