Algebra Solver and Math Simplifier that SHOWS WORK

Algebra ->  Graphical Expression Rendering -> Algebra Solver and Math Simplifier that SHOWS WORK      Log On


   
Plot a formula | 
Expression Simplifier and Solver
 | 


YOUR ANSWER


  • Graphical form: %286%2Aa%5E2%2B1%29%2A%282%2Aa%5E2%2B3%29 simplifies to 12%2Aa%5E%284%29%2B20%2Aa%5E2%2B3
  • Text form: (6*a^2+1)*(2*a^2+3) simplifies to 12*a^(4)+20*a^2+3
  • Cartoon (animation) form: simplify_cartoon%28+%286%2Aa%5E2%2B1%29%2A%282%2Aa%5E2%2B3%29+%29
    For tutors: simplify_cartoon( (6*a^2+1)*(2*a^2+3) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%286%2Aa%5E2%2B1%29%2A%282%2Aa%5E2%2B3%29+%29.
Expanded term %282%2Aa%5E2%2B3%29 by using associative property on %286%2Aa%5E2%2B1%29
It becomes .
Look at %282%2Aa%5E2%2B3%29%2A6%2Aa%5E2%2B%282%2Aa%5E2%2B3%29%2Ahighlight_red%28+1+%29.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes %282%2Aa%5E2%2B3%29%2A6%2Aa%5E2%2B%282%2Aa%5E2%2B3%29.
Look at %282%2Aa%5E2%2B3%29%2A6%2Aa%5E2%2Bhighlight_red%28+%282%2Aa%5E2%2B3%29+%29.
Remove unneeded parentheses around terms highlight_red%28+2%2Aa%5E2+%29,highlight_red%28+3+%29
It becomes .
Look at highlight_red%28+%282%2Aa%5E2%2B3%29%2A6%2Aa%5E2+%29%2B2%2Aa%5E2%2B3.
Expanded term 6%2Aa%5E2 by using associative property on %282%2Aa%5E2%2B3%29
It becomes .
Look at .
Multiplied numerator integers
It becomes highlight_green%28+12+%29%2Aa%5E2%2Aa%5E2%2B6%2Aa%5E2%2A3%2B2%2Aa%5E2%2B3.
Look at 12%2Aa%5E2%2Aa%5E2%2Bhighlight_red%28+6+%29%2Aa%5E2%2Ahighlight_red%28+3+%29%2B2%2Aa%5E2%2B3.
Multiplied numerator integers
It becomes 12%2Aa%5E2%2Aa%5E2%2Bhighlight_green%28+18+%29%2Aa%5E2%2B2%2Aa%5E2%2B3.
Look at 12%2Ahighlight_red%28+a%5E2+%29%2Ahighlight_red%28+a%5E2+%29%2B18%2Aa%5E2%2B2%2Aa%5E2%2B3.
Reduce similar several occurrences of highlight_red%28+a%5E2+%29 to highlight_green%28+a%5E%282%2B2%29+%29
It becomes 12%2Ahighlight_green%28+a%5E%282%2B2%29+%29%2B18%2Aa%5E2%2B2%2Aa%5E2%2B3.
Look at 12%2Aa%5E%28highlight_red%28+2+%29%2Bhighlight_red%28+2+%29%29%2B18%2Aa%5E2%2B2%2Aa%5E2%2B3.
Added fractions or integers together
It becomes 12%2Aa%5E%28highlight_green%28+4+%29%29%2B18%2Aa%5E2%2B2%2Aa%5E2%2B3.
Look at 12%2Aa%5E%284%29%2Bhighlight_red%28+18%2Aa%5E2+%29%2Bhighlight_red%28+2%2Aa%5E2+%29%2B3.
Eliminated similar terms highlight_red%28+18%2Aa%5E2+%29,highlight_red%28+2%2Aa%5E2+%29 replacing them with highlight_green%28+%2818%2B2%29%2Aa%5E2+%29
It becomes 12%2Aa%5E%284%29%2Bhighlight_green%28+%2818%2B2%29%2Aa%5E2+%29%2B3.
Look at 12%2Aa%5E%284%29%2B%28highlight_red%28+18+%29%2Bhighlight_red%28+2+%29%29%2Aa%5E2%2B3.
Added fractions or integers together
It becomes 12%2Aa%5E%284%29%2B%28highlight_green%28+20+%29%29%2Aa%5E2%2B3.
Look at 12%2Aa%5E%284%29%2Bhighlight_red%28+%28highlight_red%28+20+%29%29%2Aa%5E2+%29%2B3.
Remove unneeded parentheses around factor highlight_red%28+20+%29
It becomes 12%2Aa%5E%284%29%2Bhighlight_green%28+20+%29%2Aa%5E2%2B3.
Result: 12%2Aa%5E%284%29%2B20%2Aa%5E2%2B3

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.

Algebra.Com's Home Page.

This simplifier has been used 37272711 times.