SOLUTION: simplify the expression -2(4y^2+3z^3+5)+3(2y^2-5z^3+3).

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Question 632405: simplify the expression -2(4y^2+3z^3+5)+3(2y^2-5z^3+3).
Answer by 55305(86) About Me  (Show Source):
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Solved by pluggable solver: EXPLAIN simplification of an expression
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YOUR ANSWER


  • 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.

DETAILED EXPLANATION

Look at .
Expanded term -2 by using associative property on %284%2Ay%5E2%2B3%2Az%5E3%2B5%29
It becomes .
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.
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.
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.
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.
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 .
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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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Done!