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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

Factoring

Solve

Calculus: Integration, Differentiation, and Limits

Differential Equations

Matrix Inverse

Eigenvalues

Eigenvectors

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.

withStudent:-Basics:

LongDivision48x4+284x3+620x2+593x+210,2x+3

%+2x,3x2224x3+106x2+151x+70)x2148x41+284x31+620x21+593x1+21048x4+72x3.212x3+620x2212x3+318x2.302x2+593x302x2+453x.140x+210140x+210.0

(1.1)

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

(1.2)

Factoring

The FactorSteps command shows the steps in factoring a polynomial.

withStudent:-Basics:

FactorStepsx3+6x2+12x+8

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:

(2.1)

Solve

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

withStudent:-Basics:

SolveSteps5ⅇ4x=16