document.write( "Question 155240: I need to understand this by having it written out and simplified for me. Thank you.\r
\n" ); document.write( "\n" ); document.write( " 3. A rectangular box is (4x + 3) feet wide, (5x - 2) feet long, and (3x + 2) feet high. Find the volume of this box. \n" ); document.write( "
Algebra.Com's Answer #114295 by nerdybill(7384)\"\" \"About 
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A rectangular box is (4x + 3) feet wide, (5x - 2) feet long, and (3x + 2) feet high. Find the volume of this box.
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\n" ); document.write( "The volume of ANY rectangular box is:
\n" ); document.write( "length * width * height
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\n" ); document.write( "The problem gives us:
\n" ); document.write( "width is (4x + 3) feet
\n" ); document.write( "length is (5x - 2) feet
\n" ); document.write( "height is (3x + 2) feet
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\n" ); document.write( "Therefore the volume is:
\n" ); document.write( "(4x + 3)(5x - 2)(3x + 2)
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\n" ); document.write( "Now, we must multiply the three polynomials together. Let's start by multiplying the first two terms together. We do this by applying \"FOIL\". FOIL is a memory aid to remind you how to multiply them together.
\n" ); document.write( "Looking at our first two terms and applying FOIL:
\n" ); document.write( "(4x + 3)(5x - 2)
\n" ); document.write( "F: multiply First terms: (4x)(5x) = 20x^2
\n" ); document.write( "O: multiply Outer terms: (4x)(-2) = -8x
\n" ); document.write( "I: multiply Inner terms: (3)(5x) = 15x
\n" ); document.write( "L: multiply Last terms: (3)(-2) = -6
\n" ); document.write( "Finally, combine all results:
\n" ); document.write( "20x^2 -8x +15x -6
\n" ); document.write( "20x^2 + 7x -6
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\n" ); document.write( "Recapping:
\n" ); document.write( "(4x + 3)(5x - 2)(3x + 2)
\n" ); document.write( "= (20x^2 + 7x -6)(3x + 2)
\n" ); document.write( "= (20x^2 + 7x -6)(3x) + (20x^2 + 7x -6)(2)
\n" ); document.write( "= (60x^3 + 21x^2 - 18x) + (40x^2 + 14x -12)
\n" ); document.write( "= 60x^3 + 21x^2 - 18x + 40x^2 + 14x -12
\n" ); document.write( "= 60x^3 + (21x^2 + 40x^2) + (-18x + 14x) -12
\n" ); document.write( "= 60x^3 + (61x^2) + (-4x) -12
\n" ); document.write( "= 60x^3 + 61x^2 - 4x -12 cubic feet (this is the solution)\r
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