SOLUTION: Dear Tutor, It would be really very nice of you to evaluate this question for me. Evaluate: 2a-{4[b-3(a-2xb-2a)]-10(3b-5a)] Thank you

Algebra ->  Expressions -> SOLUTION: Dear Tutor, It would be really very nice of you to evaluate this question for me. Evaluate: 2a-{4[b-3(a-2xb-2a)]-10(3b-5a)] Thank you      Log On


   

Question 6788: Dear Tutor,
It would be really very nice of you to evaluate this question for me.
Evaluate:
2a-{4[b-3(a-2xb-2a)]-10(3b-5a)]
Thank you
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: 2a-%284%2A%28b-3%2A%28a-2xb-2a%29%29-10%2A%283b-5a%29%29 simplifies to -60%2Aa%2B26%2Ab-24%2Axb
  • Text form: 2a-(4*(b-3*(a-2xb-2a))-10*(3b-5a)) simplifies to -60*a+26*b-24*xb
  • Cartoon (animation) form: simplify_cartoon%28+2a-%284%2A%28b-3%2A%28a-2xb-2a%29%29-10%2A%283b-5a%29%29+%29
    For tutors: simplify_cartoon( 2a-(4*(b-3*(a-2xb-2a))-10*(3b-5a)) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 2%2Aa-highlight_red%28+%284%2A%28b-3%2A%28a-2%2Axb-2%2Aa%29%29-10%2A%283%2Ab-5%2Aa%29%29+%29.
Remove unneeded parentheses around terms highlight_red%28+-4%2A%28b-3%2A%28a-2%2Axb-2%2Aa%29%29+%29,highlight_red%28+10%2A%283%2Ab-5%2Aa%29+%29
It becomes .
Look at .
Eliminated similar terms highlight_red%28+a+%29,highlight_red%28+-2%2Aa+%29 replacing them with highlight_green%28+%281-2%29%2Aa+%29
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Removed extra sign in front of -1
It becomes .
Look at .
Remove unneeded parentheses around factor highlight_red%28+1+%29
It becomes 2%2Aa-4%2A%28b-3%2A%28-highlight_green%28+1+%29%2Aa-2%2Axb%29%29%2B10%2A%283%2Ab-5%2Aa%29.
Look at 2%2Aa-4%2A%28b-3%2A%28-highlight_red%28+1+%29%2Aa-2%2Axb%29%29%2B10%2A%283%2Ab-5%2Aa%29.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes 2%2Aa-4%2A%28b-3%2A%28-a-2%2Axb%29%29%2B10%2A%283%2Ab-5%2Aa%29.
Look at 2%2Aa-4%2A%28b-highlight_red%28+3%2A%28-a-2%2Axb%29+%29%29%2B10%2A%283%2Ab-5%2Aa%29.
Expanded term -3 by using associative property on %28-a-2%2Axb%29
It becomes .
Look at 2%2Aa-highlight_red%28+4%2A%28b%2B3%2Aa%2B3%2A2%2Axb%29+%29%2B10%2A%283%2Ab-5%2Aa%29.
Expanded term -4 by using associative property on %28b%2B3%2Aa%2B3%2A2%2Axb%29
It becomes .
Look at .
Multiplied numerator integers
It becomes 2%2Aa-4%2Ab-highlight_green%28+12+%29%2Aa-4%2A3%2A2%2Axb%2B10%2A%283%2Ab-5%2Aa%29.
Look at .
Multiplied numerator integers
It becomes 2%2Aa-4%2Ab-12%2Aa-highlight_green%28+24+%29%2Axb%2B10%2A%283%2Ab-5%2Aa%29.
Look at .
Eliminated similar terms highlight_red%28+2%2Aa+%29,highlight_red%28+-12%2Aa+%29 replacing them with highlight_green%28+%282-12%29%2Aa+%29
It becomes highlight_green%28+%282-12%29%2Aa+%29-4%2Ab-24%2Axb%2B10%2A%283%2Ab-5%2Aa%29.
Look at .
Added fractions or integers together
It becomes %28highlight_green%28+-10+%29%29%2Aa-4%2Ab-24%2Axb%2B10%2A%283%2Ab-5%2Aa%29.
Look at %28highlight_red%28+-10+%29%29%2Aa-4%2Ab-24%2Axb%2B10%2A%283%2Ab-5%2Aa%29.
Removed extra sign in front of -10
It becomes %28-highlight_green%28+10+%29%29%2Aa-4%2Ab-24%2Axb%2B10%2A%283%2Ab-5%2Aa%29.
Look at .
Remove unneeded parentheses around factor highlight_red%28+10+%29
It becomes -highlight_green%28+10+%29%2Aa-4%2Ab-24%2Axb%2B10%2A%283%2Ab-5%2Aa%29.
Look at -10%2Aa-4%2Ab-24%2Axb%2Bhighlight_red%28+10%2A%283%2Ab-5%2Aa%29+%29.
Expanded term 10 by using associative property on %283%2Ab-5%2Aa%29
It becomes -10%2Aa-4%2Ab-24%2Axb%2Bhighlight_green%28+10%2A3%2Ab+%29-highlight_green%28+10%2A5%2Aa+%29.
Look at -10%2Aa-4%2Ab-24%2Axb%2Bhighlight_red%28+10+%29%2Ahighlight_red%28+3+%29%2Ab-10%2A5%2Aa.
Multiplied numerator integers
It becomes -10%2Aa-4%2Ab-24%2Axb%2Bhighlight_green%28+30+%29%2Ab-10%2A5%2Aa.
Look at -10%2Aa-4%2Ab-24%2Axb%2B30%2Ab-highlight_red%28+10+%29%2Ahighlight_red%28+5+%29%2Aa.
Multiplied numerator integers
It becomes -10%2Aa-4%2Ab-24%2Axb%2B30%2Ab-highlight_green%28+50+%29%2Aa.
Look at -highlight_red%28+10%2Aa+%29-4%2Ab-24%2Axb%2B30%2Ab-highlight_red%28+50%2Aa+%29.
Eliminated similar terms highlight_red%28+-10%2Aa+%29,highlight_red%28+-50%2Aa+%29 replacing them with highlight_green%28+%28-10-50%29%2Aa+%29
It becomes highlight_green%28+%28-10-50%29%2Aa+%29-4%2Ab-24%2Axb%2B30%2Ab.
Look at %28-10-50%29%2Aa-highlight_red%28+4%2Ab+%29-24%2Axb%2Bhighlight_red%28+30%2Ab+%29.
Eliminated similar terms highlight_red%28+-4%2Ab+%29,highlight_red%28+30%2Ab+%29 replacing them with highlight_green%28+%28-4%2B30%29%2Ab+%29
It becomes %28-10-50%29%2Aa%2Bhighlight_green%28+%28-4%2B30%29%2Ab+%29-24%2Axb.
Look at %28-highlight_red%28+10+%29-highlight_red%28+50+%29%29%2Aa%2B%28-4%2B30%29%2Ab-24%2Axb.
Added fractions or integers together
It becomes %28highlight_green%28+-60+%29%29%2Aa%2B%28-4%2B30%29%2Ab-24%2Axb.
Look at %28-60%29%2Aa%2B%28-highlight_red%28+4+%29%2Bhighlight_red%28+30+%29%29%2Ab-24%2Axb.
Added fractions or integers together
It becomes %28-60%29%2Aa%2B%28highlight_green%28+26+%29%29%2Ab-24%2Axb.
Look at %28highlight_red%28+-60+%29%29%2Aa%2B%2826%29%2Ab-24%2Axb.
Removed extra sign in front of -60
It becomes %28-highlight_green%28+60+%29%29%2Aa%2B%2826%29%2Ab-24%2Axb.
Look at highlight_red%28+%28-highlight_red%28+60+%29%29%2Aa+%29%2B%2826%29%2Ab-24%2Axb.
Remove unneeded parentheses around factor highlight_red%28+60+%29
It becomes -highlight_green%28+60+%29%2Aa%2B%2826%29%2Ab-24%2Axb.
Look at -60%2Aa%2Bhighlight_red%28+%28highlight_red%28+26+%29%29%2Ab+%29-24%2Axb.
Remove unneeded parentheses around factor highlight_red%28+26+%29
It becomes -60%2Aa%2Bhighlight_green%28+26+%29%2Ab-24%2Axb.
Result: -60%2Aa%2B26%2Ab-24%2Axb

Universal Simplifier and Solver


Done!