Algebra Solver and Math Simplifier that SHOWS WORK

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Expression Simplifier and Solver
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YOUR ANSWER


  • Graphical form: %28x-13%2Ai%29%2A%28x%2B13%2Ai%29 simplifies to x%5E2-169%2Ai%5E2
  • Text form: (x-13*i)*(x+13*i) simplifies to x^2-169*i^2
  • Cartoon (animation) form: simplify_cartoon%28+%28x-13%2Ai%29%2A%28x%2B13%2Ai%29+%29
    For tutors: simplify_cartoon( (x-13*i)*(x+13*i) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%28x-13%2Ai%29%2A%28x%2B13%2Ai%29+%29.
Expanded term %28x%2B13%2Ai%29 by using associative property on %28x-13%2Ai%29
It becomes highlight_green%28+%28x%2B13%2Ai%29%2Ax+%29-highlight_green%28+%28x%2B13%2Ai%29%2A13%2Ai+%29.
Look at highlight_red%28+%28x%2B13%2Ai%29%2Ax+%29-%28x%2B13%2Ai%29%2A13%2Ai.
Expanded term x by using associative property on %28x%2B13%2Ai%29
It becomes highlight_green%28+x%2Ax+%29%2Bhighlight_green%28+x%2A13%2Ai+%29-%28x%2B13%2Ai%29%2A13%2Ai.
Look at highlight_red%28+x+%29%2Ahighlight_red%28+x+%29%2Bx%2A13%2Ai-%28x%2B13%2Ai%29%2A13%2Ai.
Reduce similar several occurrences of highlight_red%28+x+%29 to highlight_green%28+x%5E2+%29
It becomes highlight_green%28+x%5E2+%29%2Bx%2A13%2Ai-%28x%2B13%2Ai%29%2A13%2Ai.
Look at x%5E2%2Bx%2A13%2Ai-highlight_red%28+%28x%2B13%2Ai%29%2A13%2Ai+%29.
Expanded term -13%2Ai by using associative property on %28x%2B13%2Ai%29
It becomes x%5E2%2Bx%2A13%2Ai-highlight_green%28+13%2Ai%2Ax+%29-highlight_green%28+13%2Ai%2A13%2Ai+%29.
Look at x%5E2%2Bx%2A13%2Ai-13%2Ai%2Ax-highlight_red%28+13+%29%2Ai%2Ahighlight_red%28+13+%29%2Ai.
Multiplied numerator integers
It becomes x%5E2%2Bx%2A13%2Ai-13%2Ai%2Ax-highlight_green%28+169+%29%2Ai%2Ai.
Look at x%5E2%2Bx%2A13%2Ai-13%2Ai%2Ax-169%2Ahighlight_red%28+i+%29%2Ahighlight_red%28+i+%29.
Reduce similar several occurrences of highlight_red%28+i+%29 to highlight_green%28+i%5E2+%29
It becomes x%5E2%2Bx%2A13%2Ai-13%2Ai%2Ax-169%2Ahighlight_green%28+i%5E2+%29.
Look at x%5E2%2Bhighlight_red%28+x%2A13%2Ai+%29-highlight_red%28+13%2Ai%2Ax+%29-169%2Ai%5E2.
Eliminated similar terms highlight_red%28+x%2A13%2Ai+%29,highlight_red%28+-13%2Ai%2Ax+%29 replacing them with highlight_green%28+%2813-13%29%2Ax%2Ai+%29
It becomes x%5E2%2Bhighlight_green%28+%2813-13%29%2Ax%2Ai+%29-169%2Ai%5E2.
Look at x%5E2%2Bhighlight_red%28+%2813-13%29%2Ax%2Ai+%29-169%2Ai%5E2.
Since highlight_red%28+%2813-13%29%2Ax%2Ai+%29 has zero as a factor, it should be replaced with a zero
Look at x%5E2%2B0-169%2Ai%5E2.
Added fractions or integers together
It becomes x%5E2%2B0-169%2Ai%5E2.
Look at x%5E2%2Bhighlight_red%28+0+%29-169%2Ai%5E2.
Remove extraneous zero highlight_red%28+0+%29
It becomes x%5E2-169%2Ai%5E2.
Result: x%5E2-169%2Ai%5E2

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 37280831 times.