Algebra Solver and Math Simplifier that SHOWS WORK

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Expression Simplifier and Solver
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YOUR ANSWER


  • Graphical form: %282%2Aa-1%29%2A%288%2Aa-5%29 simplifies to 16%2Aa%5E2-18%2Aa%2B5
  • Text form: (2*a-1)*(8*a-5) simplifies to 16*a^2-18*a+5
  • Cartoon (animation) form: simplify_cartoon%28+%282%2Aa-1%29%2A%288%2Aa-5%29+%29
    For tutors: simplify_cartoon( (2*a-1)*(8*a-5) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%282%2Aa-1%29%2A%288%2Aa-5%29+%29.
Expanded term %288%2Aa-5%29 by using associative property on %282%2Aa-1%29
It becomes highlight_green%28+%288%2Aa-5%29%2A2%2Aa+%29-highlight_green%28+%288%2Aa-5%29%2A1+%29.
Look at %288%2Aa-5%29%2A2%2Aa-%288%2Aa-5%29%2Ahighlight_red%28+1+%29.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes %288%2Aa-5%29%2A2%2Aa-%288%2Aa-5%29.
Look at %288%2Aa-5%29%2A2%2Aa-highlight_red%28+%288%2Aa-5%29+%29.
Remove unneeded parentheses around terms highlight_red%28+-8%2Aa+%29,highlight_red%28+5+%29
It becomes %288%2Aa-5%29%2A2%2Aa-highlight_green%28+8%2Aa+%29%2Bhighlight_green%28+5+%29.
Look at highlight_red%28+%288%2Aa-5%29%2A2%2Aa+%29-8%2Aa%2B5.
Expanded term 2%2Aa by using associative property on %288%2Aa-5%29
It becomes highlight_green%28+2%2Aa%2A8%2Aa+%29-highlight_green%28+2%2Aa%2A5+%29-8%2Aa%2B5.
Look at highlight_red%28+2+%29%2Aa%2Ahighlight_red%28+8+%29%2Aa-2%2Aa%2A5-8%2Aa%2B5.
Multiplied numerator integers
It becomes highlight_green%28+16+%29%2Aa%2Aa-2%2Aa%2A5-8%2Aa%2B5.
Look at 16%2Aa%2Aa-highlight_red%28+2+%29%2Aa%2Ahighlight_red%28+5+%29-8%2Aa%2B5.
Multiplied numerator integers
It becomes 16%2Aa%2Aa-highlight_green%28+10+%29%2Aa-8%2Aa%2B5.
Look at 16%2Ahighlight_red%28+a+%29%2Ahighlight_red%28+a+%29-10%2Aa-8%2Aa%2B5.
Reduce similar several occurrences of highlight_red%28+a+%29 to highlight_green%28+a%5E2+%29
It becomes 16%2Ahighlight_green%28+a%5E2+%29-10%2Aa-8%2Aa%2B5.
Look at 16%2Aa%5E2-highlight_red%28+10%2Aa+%29-highlight_red%28+8%2Aa+%29%2B5.
Eliminated similar terms highlight_red%28+-10%2Aa+%29,highlight_red%28+-8%2Aa+%29 replacing them with highlight_green%28+%28-10-8%29%2Aa+%29
It becomes 16%2Aa%5E2%2Bhighlight_green%28+%28-10-8%29%2Aa+%29%2B5.
Look at 16%2Aa%5E2%2B%28-highlight_red%28+10+%29-highlight_red%28+8+%29%29%2Aa%2B5.
Added fractions or integers together
It becomes 16%2Aa%5E2%2B%28highlight_green%28+-18+%29%29%2Aa%2B5.
Look at 16%2Aa%5E2%2B%28highlight_red%28+-18+%29%29%2Aa%2B5.
Removed extra sign in front of -18
It becomes 16%2Aa%5E2%2B%28-highlight_green%28+18+%29%29%2Aa%2B5.
Look at 16%2Aa%5E2%2Bhighlight_red%28+%28-highlight_red%28+18+%29%29%2Aa+%29%2B5.
Remove unneeded parentheses around factor highlight_red%28+18+%29
It becomes 16%2Aa%5E2-highlight_green%28+18+%29%2Aa%2B5.
Result: 16%2Aa%5E2-18%2Aa%2B5

Universal Simplifier and Solver

Welcome to Graphical Universal Mathematical Expression Simplifier and Algebra Solver (GUMESS).
It solves most middle school algebra equations and simplifies expressions, and it SHOWS ALL WORK. It is free to use.

Enter expression to be simplified, or equation to be solved.
I will figure out if what you typed is an equation.

Enter Expression ==>     
Examples: x^2-2x=-1, 3x-x-x+a-a=5, (x^2-1)/(x+1), 2x-(x+x)


Single letter variables only, no functions, xy means x*y, x(x-1) means x*(x-1), sin(x) means s*i*n*(x)


You must use the "*" (star) symbol for all multiplications! x(x+1) is WRONG! It means a function x of x-1. x*(x-1) is right. Use the ^ (caret) for exponentiation. x^2 means x squared. x/2y means x%2F2y
Resources: Simplifier Portal, help with entering simplifier formulas (a must read).


Or, click on any of these examples: 1, 2-1, 2%5E2-4%5E1, %281%29, -%28-1%29, %28%28%28%28x%29%29%29%29-x, -%28-%28-%28-%28-%28x%29%29%29%29%29%2Bx, %28%28%28%28x%29%29%29%29-y%2Ax%2A2%2Fy, %28x%2B1%29%2F%28x%2B1%29, %281%2Bx%29%2F%28x%2B1%29, %281%2Bx%29%2F%282%2A%28x%2B1%29%29, x-x%2Bx, x%2A%28y%2Az%29+-+%28x%2Ay%29%2Az, %28x-1%29%2A%28y-1%29-%28y-1%29%2A%28x-1%29, %28x-1%29%2A%28y-1%29-%28%28y-1%29%2Fx%29%5E%282-1%29%2A%28x-1%29%2Ax, 2%2A2%2A2%5E2%2Ax-x, 1%2F%282%2Bx%2Ay-y%2Ax%5E2%2F%28x%2B0%29%29, x%5E%28y%2Bz%29-x%5E%28z%2By%29, x-x%2F2, x=x, x%2B1=2, 0=5-x-7, %28x%5E2-x-2%29%2F%28%28x%2B1%29%2F%282x%2B2%29%29=0, %28x-1%29%28x-2%29%2F%28x%2B1%29=0, %28x%5E2-x-2%29=0, %28x%5E2-x-2%29%2A%28x%5E2-x-2%29%2F%28x%5E2%2B2%2Ax%2B1%29%2F%28x%5E2-4%2Ax%2B4%29, %28x%5E3-x%29%2Fx=0, %28x-1%29%2Fx=0, %282x%5E4-2%29%2F%28x-1%29=0, x%5E5-x%5E3=0, %28x-3%29%2A%28x%5E6-2x%5E3%2B1%29=0, , x%2A%28x-1%29%28x%2B1%29%2A%28x%5E3%2Bx%29, %28x-1%29%28x%2B1%29-3=0, %28x%5E2-1%29%28x%5E2%2B1%29-15=0, 1%2Fx%5E-1, x%2Fa%5E%28-5%29, x%2Aa%5E%28-5%29, x%5E-1, 2%2F6, 1%2F2-2%2F3, 1%2F2-1, 1%2F2-1%2B1%2F10, 1%2F2%2B2%2F3, 1%2F3%2B0.51, 1%2F3%2B0.5, x-x%2F3, 0.5x-x%2F3, 0.5x-2%2Ax%2F3, 1%2F2%2B1%2F3%2B1%2F6, %282x%2B2y%29%2F2, %28%28-4%2B10%29-%28-2%2B14%29%29%2F2%2A%282%29.
Please write to Igor Chudov, ichudov @ algebra.com, with questions or suggestions.

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This simplifier has been used 37899396 times.