document.write( "Question 632405: simplify the expression -2(4y^2+3z^3+5)+3(2y^2-5z^3+3). \n" ); document.write( "

Algebra.Com's Answer #398260 by 55305(86) $\"\"$ $\"About$

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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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Graphical form: $\"-2%2A%284y%5E2%2B3z%5E3%2B5%29%2B3%2A%282y%5E2-5z%5E3%2B3%29\"$ simplifies to $\"-2%2Ay%5E2-21%2Az%5E3-1\"$
Text form: -2*(4y^2+3z^3+5)+3*(2y^2-5z^3+3) simplifies to -2*y^2-21*z^3-1
Cartoon (animation) form: $\"simplify_cartoon%28+-2%2A%284y%5E2%2B3z%5E3%2B5%29%2B3%2A%282y%5E2-5z%5E3%2B3%29+%29\"$
For tutors: simplify_cartoon( -2*(4y^2+3z^3+5)+3*(2y^2-5z^3+3) )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at

.
Expanded term $\"-2\"$ by using associative property on $\"%284%2Ay%5E2%2B3%2Az%5E3%2B5%29\"$
It becomes

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Look at

.
Multiplied numerator integers
It becomes $\"-highlight_green%28+8+%29%2Ay%5E2-2%2A3%2Az%5E3-2%2A5%2B3%2A%282%2Ay%5E2-5%2Az%5E3%2B3%29\"$ .
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Look at

.
Multiplied numerator integers
It becomes $\"-8%2Ay%5E2-highlight_green%28+6+%29%2Az%5E3-2%2A5%2B3%2A%282%2Ay%5E2-5%2Az%5E3%2B3%29\"$ .
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Look at

.
Multiplied numerator integers
It becomes $\"-8%2Ay%5E2-6%2Az%5E3-highlight_green%28+10+%29%2B3%2A%282%2Ay%5E2-5%2Az%5E3%2B3%29\"$ .
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Look at $\"-8%2Ay%5E2-6%2Az%5E3-highlight_red%28+10+%29%2B3%2A%282%2Ay%5E2-5%2Az%5E3%2B3%29\"$ .
Moved $\"-10\"$ to the right of expression
It becomes $\"-8%2Ay%5E2-6%2Az%5E3%2B3%2A%282%2Ay%5E2-5%2Az%5E3%2B3%29-highlight_green%28+10+%29\"$ .
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Look at $\"-8%2Ay%5E2-6%2Az%5E3%2Bhighlight_red%28+3%2A%282%2Ay%5E2-5%2Az%5E3%2B3%29+%29-10\"$ .
Expanded term $\"3\"$ by using associative property on $\"%282%2Ay%5E2-5%2Az%5E3%2B3%29\"$
It becomes

.
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Look at

.
Multiplied numerator integers
It becomes $\"-8%2Ay%5E2-6%2Az%5E3%2Bhighlight_green%28+6+%29%2Ay%5E2-3%2A5%2Az%5E3%2B3%2A3-10\"$ .
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Look at

.
Multiplied numerator integers
It becomes $\"-8%2Ay%5E2-6%2Az%5E3%2B6%2Ay%5E2-highlight_green%28+15+%29%2Az%5E3%2B3%2A3-10\"$ .
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Look at

.
Multiplied numerator integers
It becomes $\"-8%2Ay%5E2-6%2Az%5E3%2B6%2Ay%5E2-15%2Az%5E3%2Bhighlight_green%28+9+%29-10\"$ .
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Look at $\"-8%2Ay%5E2-6%2Az%5E3%2B6%2Ay%5E2-15%2Az%5E3%2Bhighlight_red%28+9+%29-highlight_red%28+10+%29\"$ .
Added fractions or integers together
It becomes $\"-8%2Ay%5E2-6%2Az%5E3%2B6%2Ay%5E2-15%2Az%5E3%2Bhighlight_green%28+-1+%29\"$ .
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Look at $\"-8%2Ay%5E2-6%2Az%5E3%2B6%2Ay%5E2-15%2Az%5E3%2Bhighlight_red%28+-1+%29\"$ .
Removed extra sign in front of $\"-1\"$
It becomes $\"-8%2Ay%5E2-6%2Az%5E3%2B6%2Ay%5E2-15%2Az%5E3-highlight_green%28+1+%29\"$ .
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Look at $\"-highlight_red%28+8%2Ay%5E2+%29-6%2Az%5E3%2Bhighlight_red%28+6%2Ay%5E2+%29-15%2Az%5E3-1\"$ .
Eliminated similar terms $\"highlight_red%28+-8%2Ay%5E2+%29\"$ , $\"highlight_red%28+6%2Ay%5E2+%29\"$ replacing them with $\"highlight_green%28+%28-8%2B6%29%2Ay%5E2+%29\"$
It becomes $\"highlight_green%28+%28-8%2B6%29%2Ay%5E2+%29-6%2Az%5E3-15%2Az%5E3-1\"$ .
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Look at $\"%28-8%2B6%29%2Ay%5E2-highlight_red%28+6%2Az%5E3+%29-highlight_red%28+15%2Az%5E3+%29-1\"$ .
Eliminated similar terms $\"highlight_red%28+-6%2Az%5E3+%29\"$ , $\"highlight_red%28+-15%2Az%5E3+%29\"$ replacing them with $\"highlight_green%28+%28-6-15%29%2Az%5E3+%29\"$
It becomes $\"%28-8%2B6%29%2Ay%5E2%2Bhighlight_green%28+%28-6-15%29%2Az%5E3+%29-1\"$ .
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Look at $\"%28-highlight_red%28+8+%29%2Bhighlight_red%28+6+%29%29%2Ay%5E2%2B%28-6-15%29%2Az%5E3-1\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+-2+%29%29%2Ay%5E2%2B%28-6-15%29%2Az%5E3-1\"$ .
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Look at $\"%28-2%29%2Ay%5E2%2B%28-highlight_red%28+6+%29-highlight_red%28+15+%29%29%2Az%5E3-1\"$ .
Added fractions or integers together
It becomes $\"%28-2%29%2Ay%5E2%2B%28highlight_green%28+-21+%29%29%2Az%5E3-1\"$ .
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Look at $\"%28highlight_red%28+-2+%29%29%2Ay%5E2%2B%28-21%29%2Az%5E3-1\"$ .
Removed extra sign in front of $\"-2\"$
It becomes $\"%28-highlight_green%28+2+%29%29%2Ay%5E2%2B%28-21%29%2Az%5E3-1\"$ .
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Look at $\"%28-2%29%2Ay%5E2%2B%28highlight_red%28+-21+%29%29%2Az%5E3-1\"$ .
Removed extra sign in front of $\"-21\"$
It becomes $\"%28-2%29%2Ay%5E2%2B%28-highlight_green%28+21+%29%29%2Az%5E3-1\"$ .
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Look at $\"highlight_red%28+%28-highlight_red%28+2+%29%29%2Ay%5E2+%29%2B%28-21%29%2Az%5E3-1\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+2+%29\"$
It becomes $\"-highlight_green%28+2+%29%2Ay%5E2%2B%28-21%29%2Az%5E3-1\"$ .
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Look at $\"-2%2Ay%5E2%2Bhighlight_red%28+%28-highlight_red%28+21+%29%29%2Az%5E3+%29-1\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+21+%29\"$
It becomes $\"-2%2Ay%5E2-highlight_green%28+21+%29%2Az%5E3-1\"$ .
Result: $\"-2%2Ay%5E2-21%2Az%5E3-1\"$
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Universal Simplifier and Solver

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Done!

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