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Solution Steps

Maple 2021 includes numerous new algorithms for showing step-by-step solutions for a variety of problems in mathematics.


Long Division



Calculus: Integration, Differentiation, and Limits

Differential Equations

Matrix Inverse



Gauss Jordan Elimination

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Long Division

The LongDivision command gives a visual solution to an arithmetic or polynomial long division problem, showing all of the intermediate steps.





LongDivision1001,30, 'decimaldigits'=4;

 — — — —3—3—.—3—6—6—6— 30 ) 1001.0000       9—0—       101        9—0—        110         9—0—         200         1—8—0—          200          1—8—0—           200           1—8—0—            20



The FactorSteps command shows the steps in factoring a polynomial.



â–«1. Trial Evaluationsâ—¦Rewrite in standard formâ—¦The factors of the constant coefficient 8 are:C=1,2,4,8â—¦Trial evaluations of x in ±C find x = −2 satisfies the equation, so x+2 is a factorâ—¦Divide by x+2x22x2+4x+4)x21x31+6x21+12x1+8x3+2x2.4x2+12x4x2+8x.4x+84x+8.0â—¦Quotient times divisor from long division•2. Examine term:x2+4x+4â–«3. Apply the AC Methodâ—¦Examine quadraticâ—¦Look at the coefficients, Ax2+Bx+CA=1,B=4,C=4â—¦Find factors of |AC| = |14| = 41,2,4â—¦Find pairs of the above factors, which, when multiplied equal 4,â—¦Which pairs of these factors have a sum of B = 4? Found:=4â—¦Split the middle term to use above pairâ—¦Factor x out of the first pairâ—¦Factor 2 out of the second pairâ—¦x+2 is a common factorâ—¦Group common factorThis gives:•4. This gives:



The SolveSteps command shows the steps in solving an equation or system of equations



Let's solve=16▫Convert from exponential equation◦Divide both sides by 5=◦Simplify=165◦Apply ln to each side=◦Apply ln rule: ln(e^b) = b4x=ln165•Divide both sides by 4=•Exact solutionx=ln1654•Approximate solutionx=0.2907877025



Let's solve=18,=32•Pick the 2nd equation to solve for y=32â–«A: isolate for yâ—¦Subtract 7x from both sides=â—¦Simplify=â—¦Divide both sides by −8=â—¦Simplifyy=â—¦Solutiony=4+7x8•Substitute the value of y=4+7x8 into the 1st equation of the system=18â–«Solve for xâ—¦Evaluate subtraction and addition103x84=18â—¦Add 4 to both sides=â—¦Simplify=22â—¦Divide both sides by 1038=â—¦Simplifyx=â—¦Rewrite division as multiplication by reciprocalx=â—¦Multiply fraction and reduce by gcdx=176103•Substitute x=176103 into equation A y=â–«Solve for yâ—¦Evaluate multiplication and divisiony=â—¦Evaluate subtraction and additiony=258103•Solutionx=176103,y=258103


Calculus: Integration, Differentiation, and Limits

The ShowSolution command has been improved to show more detailed steps when solving integration, differentiation, and limit problems.

with Student:-Calculus1 :


Integration Stepssinx2ⅆxâ–«1. Rewriteâ—¦Equivalent expressionsinx2=12cos2x2This gives:12cos2x2ⅆxâ–«2. Apply the sum ruleâ—¦Recall the definition of the sum rulefx+gxⅆx