SOLUTION: Find the indicated product. -x^5y(3xy^4+3x^5y^4-x^4y)

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Question 34489: Find the indicated product.
-x^5y(3xy^4+3x^5y^4-x^4y)
Answer by ichudov(499) 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


  • Here's what you tried:
  • Graphical form: -x%5E5%2Ay%2A%283x%2Ay%5E4%2B3x%5E5%2Ay%5E4-x%5E4%2Ay%29 simplifies to -x%5E%286%29%2Ay%5E%285%29%2A3-x%5E%2810%29%2Ay%5E%285%29%2A3%2Bx%5E%289%29%2Ay%5E2
  • Text form: -x^5*y*(3x*y^4+3x^5*y^4-x^4*y) simplifies to -x^(6)*y^(5)*3-x^(10)*y^(5)*3+x^(9)*y^2
  • Cartoon (animation) form: simplify_cartoon%28+-x%5E5%2Ay%2A%283x%2Ay%5E4%2B3x%5E5%2Ay%5E4-x%5E4%2Ay%29+%29
    For tutors: simplify_cartoon( -x^5*y*(3x*y^4+3x^5*y^4-x^4*y) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at -highlight_red%28+x%5E5%2Ay%2A%283%2Ax%2Ay%5E4%2B3%2Ax%5E5%2Ay%5E4-x%5E4%2Ay%29+%29.
Expanded term -x%5E5%2Ay by using associative property on %283%2Ax%2Ay%5E4%2B3%2Ax%5E5%2Ay%5E4-x%5E4%2Ay%29
It becomes -highlight_green%28+x%5E5%2Ay%2A3%2Ax%2Ay%5E4+%29-highlight_green%28+x%5E5%2Ay%2A3%2Ax%5E5%2Ay%5E4+%29%2Bhighlight_green%28+x%5E5%2Ay%2Ax%5E4%2Ay+%29.
Look at -highlight_red%28+x%5E5+%29%2Ay%2A3%2Ahighlight_red%28+x+%29%2Ay%5E4-x%5E5%2Ay%2A3%2Ax%5E5%2Ay%5E4%2Bx%5E5%2Ay%2Ax%5E4%2Ay.
Reduce similar several occurrences of highlight_red%28+x%5E5+%29 to highlight_green%28+x%5E%281%2B5%29+%29
It becomes -highlight_green%28+x%5E%281%2B5%29+%29%2Ay%2A3%2Ay%5E4-x%5E5%2Ay%2A3%2Ax%5E5%2Ay%5E4%2Bx%5E5%2Ay%2Ax%5E4%2Ay.
Look at -x%5E%281%2B5%29%2Ahighlight_red%28+y+%29%2A3%2Ahighlight_red%28+y%5E4+%29-x%5E5%2Ay%2A3%2Ax%5E5%2Ay%5E4%2Bx%5E5%2Ay%2Ax%5E4%2Ay.
Reduce similar several occurrences of highlight_red%28+y+%29 to highlight_green%28+y%5E%281%2B4%29+%29
It becomes -x%5E%281%2B5%29%2Ahighlight_green%28+y%5E%281%2B4%29+%29%2A3-x%5E5%2Ay%2A3%2Ax%5E5%2Ay%5E4%2Bx%5E5%2Ay%2Ax%5E4%2Ay.
Look at -x%5E%281%2B5%29%2Ay%5E%281%2B4%29%2A3-highlight_red%28+x%5E5+%29%2Ay%2A3%2Ahighlight_red%28+x%5E5+%29%2Ay%5E4%2Bx%5E5%2Ay%2Ax%5E4%2Ay.
Reduce similar several occurrences of highlight_red%28+x%5E5+%29 to highlight_green%28+x%5E%285%2B5%29+%29
It becomes -x%5E%281%2B5%29%2Ay%5E%281%2B4%29%2A3-highlight_green%28+x%5E%285%2B5%29+%29%2Ay%2A3%2Ay%5E4%2Bx%5E5%2Ay%2Ax%5E4%2Ay.
Look at -x%5E%281%2B5%29%2Ay%5E%281%2B4%29%2A3-x%5E%285%2B5%29%2Ahighlight_red%28+y+%29%2A3%2Ahighlight_red%28+y%5E4+%29%2Bx%5E5%2Ay%2Ax%5E4%2Ay.
Reduce similar several occurrences of highlight_red%28+y+%29 to highlight_green%28+y%5E%281%2B4%29+%29
It becomes -x%5E%281%2B5%29%2Ay%5E%281%2B4%29%2A3-x%5E%285%2B5%29%2Ahighlight_green%28+y%5E%281%2B4%29+%29%2A3%2Bx%5E5%2Ay%2Ax%5E4%2Ay.
Look at -x%5E%281%2B5%29%2Ay%5E%281%2B4%29%2A3-x%5E%285%2B5%29%2Ay%5E%281%2B4%29%2A3%2Bhighlight_red%28+x%5E5+%29%2Ay%2Ahighlight_red%28+x%5E4+%29%2Ay.
Reduce similar several occurrences of highlight_red%28+x%5E5+%29 to highlight_green%28+x%5E%285%2B4%29+%29
It becomes -x%5E%281%2B5%29%2Ay%5E%281%2B4%29%2A3-x%5E%285%2B5%29%2Ay%5E%281%2B4%29%2A3%2Bhighlight_green%28+x%5E%285%2B4%29+%29%2Ay%2Ay.
Look at -x%5E%281%2B5%29%2Ay%5E%281%2B4%29%2A3-x%5E%285%2B5%29%2Ay%5E%281%2B4%29%2A3%2Bx%5E%285%2B4%29%2Ahighlight_red%28+y+%29%2Ahighlight_red%28+y+%29.
Reduce similar several occurrences of highlight_red%28+y+%29 to highlight_green%28+y%5E2+%29
It becomes -x%5E%281%2B5%29%2Ay%5E%281%2B4%29%2A3-x%5E%285%2B5%29%2Ay%5E%281%2B4%29%2A3%2Bx%5E%285%2B4%29%2Ahighlight_green%28+y%5E2+%29.
Look at -x%5E%28highlight_red%28+1+%29%2Bhighlight_red%28+5+%29%29%2Ay%5E%281%2B4%29%2A3-x%5E%285%2B5%29%2Ay%5E%281%2B4%29%2A3%2Bx%5E%285%2B4%29%2Ay%5E2.
Added fractions or integers together
It becomes -x%5E%28highlight_green%28+6+%29%29%2Ay%5E%281%2B4%29%2A3-x%5E%285%2B5%29%2Ay%5E%281%2B4%29%2A3%2Bx%5E%285%2B4%29%2Ay%5E2.
Look at -x%5E%286%29%2Ay%5E%28highlight_red%28+1+%29%2Bhighlight_red%28+4+%29%29%2A3-x%5E%285%2B5%29%2Ay%5E%281%2B4%29%2A3%2Bx%5E%285%2B4%29%2Ay%5E2.
Added fractions or integers together
It becomes -x%5E%286%29%2Ay%5E%28highlight_green%28+5+%29%29%2A3-x%5E%285%2B5%29%2Ay%5E%281%2B4%29%2A3%2Bx%5E%285%2B4%29%2Ay%5E2.
Look at -x%5E%286%29%2Ay%5E%285%29%2A3-x%5E%28highlight_red%28+5+%29%2Bhighlight_red%28+5+%29%29%2Ay%5E%281%2B4%29%2A3%2Bx%5E%285%2B4%29%2Ay%5E2.
Added fractions or integers together
It becomes -x%5E%286%29%2Ay%5E%285%29%2A3-x%5E%28highlight_green%28+10+%29%29%2Ay%5E%281%2B4%29%2A3%2Bx%5E%285%2B4%29%2Ay%5E2.
Look at -x%5E%286%29%2Ay%5E%285%29%2A3-x%5E%2810%29%2Ay%5E%28highlight_red%28+1+%29%2Bhighlight_red%28+4+%29%29%2A3%2Bx%5E%285%2B4%29%2Ay%5E2.
Added fractions or integers together
It becomes -x%5E%286%29%2Ay%5E%285%29%2A3-x%5E%2810%29%2Ay%5E%28highlight_green%28+5+%29%29%2A3%2Bx%5E%285%2B4%29%2Ay%5E2.
Look at -x%5E%286%29%2Ay%5E%285%29%2A3-x%5E%2810%29%2Ay%5E%285%29%2A3%2Bx%5E%28highlight_red%28+5+%29%2Bhighlight_red%28+4+%29%29%2Ay%5E2.
Added fractions or integers together
It becomes -x%5E%286%29%2Ay%5E%285%29%2A3-x%5E%2810%29%2Ay%5E%285%29%2A3%2Bx%5E%28highlight_green%28+9+%29%29%2Ay%5E2.
Result: -x%5E%286%29%2Ay%5E%285%29%2A3-x%5E%2810%29%2Ay%5E%285%29%2A3%2Bx%5E%289%29%2Ay%5E2

Universal Simplifier and Solver


Done!