SOLUTION: i need help with like-terms. here is one of my problems...... (6v^5-5v)-5(7v^5-2v-7)

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Question 6582: i need help with like-terms. here is one of my problems......
(6v^5-5v)-5(7v^5-2v-7)
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: %286v%5E5-5v%29-5%2A%287v%5E5-2v-7%29 simplifies to -29%2Av%5E5%2B5%2Av%2B35
  • Text form: (6v^5-5v)-5*(7v^5-2v-7) simplifies to -29*v^5+5*v+35
  • Cartoon (animation) form: simplify_cartoon%28+%286v%5E5-5v%29-5%2A%287v%5E5-2v-7%29+%29
    For tutors: simplify_cartoon( (6v^5-5v)-5*(7v^5-2v-7) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%286%2Av%5E5-5%2Av%29+%29-5%2A%287%2Av%5E5-2%2Av-7%29.
Remove unneeded parentheses around terms highlight_red%28+6%2Av%5E5+%29,highlight_red%28+-5%2Av+%29
It becomes highlight_green%28+6%2Av%5E5+%29-highlight_green%28+5%2Av+%29-5%2A%287%2Av%5E5-2%2Av-7%29.
Look at 6%2Av%5E5-5%2Av-highlight_red%28+5%2A%287%2Av%5E5-2%2Av-7%29+%29.
Expanded term -5 by using associative property on %287%2Av%5E5-2%2Av-7%29
It becomes .
Look at 6%2Av%5E5-5%2Av-highlight_red%28+5+%29%2Ahighlight_red%28+7+%29%2Av%5E5%2B5%2A2%2Av%2B5%2A7.
Multiplied numerator integers
It becomes 6%2Av%5E5-5%2Av-highlight_green%28+35+%29%2Av%5E5%2B5%2A2%2Av%2B5%2A7.
Look at 6%2Av%5E5-5%2Av-35%2Av%5E5%2Bhighlight_red%28+5+%29%2Ahighlight_red%28+2+%29%2Av%2B5%2A7.
Multiplied numerator integers
It becomes 6%2Av%5E5-5%2Av-35%2Av%5E5%2Bhighlight_green%28+10+%29%2Av%2B5%2A7.
Look at 6%2Av%5E5-5%2Av-35%2Av%5E5%2B10%2Av%2Bhighlight_red%28+5+%29%2Ahighlight_red%28+7+%29.
Multiplied numerator integers
It becomes 6%2Av%5E5-5%2Av-35%2Av%5E5%2B10%2Av%2Bhighlight_green%28+35+%29.
Look at highlight_red%28+6%2Av%5E5+%29-5%2Av-highlight_red%28+35%2Av%5E5+%29%2B10%2Av%2B35.
Eliminated similar terms highlight_red%28+6%2Av%5E5+%29,highlight_red%28+-35%2Av%5E5+%29 replacing them with highlight_green%28+%286-35%29%2Av%5E5+%29
It becomes highlight_green%28+%286-35%29%2Av%5E5+%29-5%2Av%2B10%2Av%2B35.
Look at %286-35%29%2Av%5E5-highlight_red%28+5%2Av+%29%2Bhighlight_red%28+10%2Av+%29%2B35.
Eliminated similar terms highlight_red%28+-5%2Av+%29,highlight_red%28+10%2Av+%29 replacing them with highlight_green%28+%28-5%2B10%29%2Av+%29
It becomes %286-35%29%2Av%5E5%2Bhighlight_green%28+%28-5%2B10%29%2Av+%29%2B35.
Look at %28highlight_red%28+6+%29-highlight_red%28+35+%29%29%2Av%5E5%2B%28-5%2B10%29%2Av%2B35.
Added fractions or integers together
It becomes %28highlight_green%28+-29+%29%29%2Av%5E5%2B%28-5%2B10%29%2Av%2B35.
Look at %28-29%29%2Av%5E5%2B%28-highlight_red%28+5+%29%2Bhighlight_red%28+10+%29%29%2Av%2B35.
Added fractions or integers together
It becomes %28-29%29%2Av%5E5%2B%28highlight_green%28+5+%29%29%2Av%2B35.
Look at %28highlight_red%28+-29+%29%29%2Av%5E5%2B%285%29%2Av%2B35.
Removed extra sign in front of -29
It becomes %28-highlight_green%28+29+%29%29%2Av%5E5%2B%285%29%2Av%2B35.
Look at highlight_red%28+%28-highlight_red%28+29+%29%29%2Av%5E5+%29%2B%285%29%2Av%2B35.
Remove unneeded parentheses around factor highlight_red%28+29+%29
It becomes -highlight_green%28+29+%29%2Av%5E5%2B%285%29%2Av%2B35.
Look at -29%2Av%5E5%2Bhighlight_red%28+%28highlight_red%28+5+%29%29%2Av+%29%2B35.
Remove unneeded parentheses around factor highlight_red%28+5+%29
It becomes -29%2Av%5E5%2Bhighlight_green%28+5+%29%2Av%2B35.
Result: -29%2Av%5E5%2B5%2Av%2B35

Universal Simplifier and Solver


Done!