document.write( "Question 629303: Can you help me figure
\n" ); document.write( "(x-1/2)(4x^3-2x^2+5x-6)\r
\n" ); document.write( "\n" ); document.write( "Where 1/2 is a fraction. I can solve this without the fraction, but can you help me to solve when there is a fraction involved. \n" ); document.write( "
Algebra.Com's Answer #396181 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
your expression is:
\n" ); document.write( "(x-1/2)(4x^3-2x^2+5x-6)
\n" ); document.write( "you use the distributive law of multiplication.
\n" ); document.write( "that law is:
\n" ); document.write( "(a + b ) * (c + d + e) equals:
\n" ); document.write( "a * (c + d + e) plus:
\n" ); document.write( "b * (c + d + e)
\n" ); document.write( "you use the distributive law of multiplication again to get:
\n" ); document.write( "a * (c + d + e) equals:
\n" ); document.write( "a*c + a*d + a*e
\n" ); document.write( "and:
\n" ); document.write( "b * (c + d + e) equals:
\n" ); document.write( "b*c + b*d + b*e.
\n" ); document.write( "put them together and you get:
\n" ); document.write( "(a + b) * (c + d + e) equals:
\n" ); document.write( "a*c + a*d + a*e + b*c + b*d + b*e
\n" ); document.write( "we can apply this to your expression of:
\n" ); document.write( "(x-1/2)(4x^3-2x^2+5x-6)
\n" ); document.write( "using the distributive law of multiplication, this becomes:
\n" ); document.write( "x*(4x^3-2x^2+5x-6) - (1/2)(4x^3-2x^2+5x-6)
\n" ); document.write( "using the distributive law of multiplication again, this becomes:
\n" ); document.write( "x*4x^3 - x*2x^2 + x*5x - x*6 - (1/2)*4x^3 + (1/2)*2x^2 - (1/2)*5x + (1/2)*6
\n" ); document.write( "simplifying each term gets you:
\n" ); document.write( "4x^4 - 2x^3 + 5x^2 - 6x -2x^3 + x^2 - (5/2)x + 3
\n" ); document.write( "you now want to combine like terms if there are any.
\n" ); document.write( "-2x^3 and -2x^3 combine into -4x^3
\n" ); document.write( "5x^2 and x^2 combine into 6x^2
\n" ); document.write( "-6x and -(5/2)x combine into (-17/2)x
\n" ); document.write( "putting all the combined terms together, you get:
\n" ); document.write( "4x^4 - 4x^3 + 6x^2 - (17/2)x + 3
\n" ); document.write( "that's your final expression.
\n" ); document.write( "i was able to confirm graphically that this expression and the starting expression are the same.
\n" ); document.write( "here's a graph of your starting expression of:
\n" ); document.write( "(x-1/2)(4x^3-2x^2+5x-6)
\n" ); document.write( "\"graph%28600%2C600%2C-10%2C10%2C-50%2C50%2C%28x-1%2F2%29%284x%5E3-2x%5E2%2B5x-6%29%29\"
\n" ); document.write( "here's a graph of your final expression of:
\n" ); document.write( "4x^4 - 4x^3 + 6x^2 - (17/2)x + 3
\n" ); document.write( "
\n" ); document.write( "here's both expressions superimposed on the same graph:
\n" ); document.write( "
\n" ); document.write( "since they superimpose on each other perfectly so that they look like one expression, they are identical to each other.
\n" ); document.write( "this confirms the solution is correct.\r
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