document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=78810>Question 78810</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Multiply.    (2x – 5y)(3x – y) </SPAN>\n" );
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document.write( "This involves variables but not substitution\r<BR>\n" );
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document.write( "This involves using variables and it involves using Distributive and Associative Laws of arithmetic and algebra\r<BR>\n" );
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document.write( "A * B + C * B = (A+C) * B   Distributive Law<BR>\n" );
document.write( "(A+B)+C = A + (B+C)<BR>\n" );
document.write( "The other law is Commutative Law, A*B = B*A \r<BR>\n" );
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document.write( "The Commutative Law can be used to write the Distributive Law another way<BR>\n" );
document.write( "A * B + A * C = A * (B + C) \r<BR>\n" );
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document.write( "In these laws A and B can be a number, a variable, or an expression.\r<BR>\n" );
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document.write( "Step 1: Distribute out the second factor\r<BR>\n" );
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document.write( "(2x – 5y)(3x – y) =  \r<BR>\n" );
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document.write( "(2x - 5y)*(3x) + (2x - 5y) * (-y)  \r<BR>\n" );
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document.write( "Step 2: Distribute out (2x - 5y) in both places\r<BR>\n" );
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document.write( "(2x)*(3x) - (5y)*(3x)  + (2x)*(-y) + (-5y)(-y)\r<BR>\n" );
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document.write( "(You may have seen a shorter pattern for this:<BR>\n" );
document.write( " (A+B)*(C+D) = A*C + A*D + B*C + B*D )\r<BR>\n" );
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document.write( "Step 3. Simplify those four terms<BR>\n" );
document.write( " 6x^2 - 15xy - 2xy + 5y^2\r<BR>\n" );
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document.write( "Step 4. Combine two like terms<BR>\n" );
document.write( " 6x^2 - 17xy + 5y^2\r<BR>\n" );
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document.write( "To learn this well, go back and look at the original expression, and the final answer, and see if you can grasp all those steps to understand how the transformation occurred.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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