After you create an expression or equation, you can transform it by changing its mathematical representation. For example, you can multiply polynomials, factor terms, simplify expressions, and combine fractions.
Original selection 

Expanded 

Multiplied out 

Multiplied out again 

You can also evaluate equations by substituting values and performing computations.
Original selection 

Expanded 

Value substituted 

Result computed 

1)Select the expression, or part of it.
2)Choose a command on the Matrices or Functions page of the Equations pod. For example, select an expression and then choose Multiply Out from the Multiplication popup menu on the Functions page.
3)To transform or evaluate an expression, use the commands on the Matrix Commands popup menu of the Matrices page and the commands on the six popup menus of the Functions page.
Matrix Transpose
Transposes the rows and columns of a selected matrix.
Selected matrix 
After transposing 



Matrix Algebra
Performs matrix multiplication and addition, and evaluates dot and cross products in a selected matrix.
Selected matrix (or matrices) 
After matrix algebra 











After performing matrix algebra, you can use the Simplify command to combine like terms.
Add Fractions
Adds selected fractions, expressing the result as a single fraction. This command also combines like terms.
Selected fraction 
After adding 







If the selected expression contains the sum of more than two fractions, Add Fractions adds only the first two. Use this command repeatedly to combine all the fractions.
Selected expression 

Added once 

Added twice 

Order Sum
Arranges polynomials in decreasing powers of a selected variable.
Before ordering 
After ordering 



Order Sum Reverse
Arranges polynomials in increasing powers of a selected variable. In the following example, you select an x—any x—before choosing Order Sum Reverse.
Before ordering 
After ordering 



Use the Multiplication popup menu on the Functions page to factor terms, multiply out expressions, and distribute multiplication and division over addition.
Factor
Factors a selected term out of a product.
Before factoring 
After factoring 





Factor Some
Factors a selected term from only those terms that contain it.
Before factoring 
After factoring 



Multiply Out
Simplifies the selected expression, distributes multiplication over addition, and expands a selected term raised to a positive integral power.
Selected expression 
After multiplying 





The Simplify command also simplifies the selected expression.
Multiply Out Once
Multiplies the first pair of factors on the left side of a selected expression.
Selected expression 
After multiplying 



If you use this command several times, the results appear in a different form.
Distribute
Performs a variety of operations depending on the expression you select, as shown in the following examples:
•Distributes division over addition.
Selected expression 
After distributing 



Use the Add Fractions command to perform the reverse operation.
•Distributes multiplication over addition.
Selected expression 
After distributing 



Use the Factor command to perform the reverse operation.
•Transforms products and quotients involving radicals and exponents into a single expression raised to a power.
Selected expression 
After distributing 







Use the Simplify command to perform the reverse operation.
Distribute Over Equality
Performs the same operation on both sides of an equal sign.
Selected expression 
After distributing 







Long Division
Performs long division in a fraction that contains a polynomial numerator and denominator.
In the following example, you select an x—any x—before choosing Long Division. You select an x in the fraction of the first result and choose Long Division again to obtain the second result.
Before dividing 

Divided once 

Divided twice 

Remove Division
Converts division to multiplication in a selected expression by changing positive exponents in a denominator to negative and negative exponents in a denominator to positive.
Selected expression 
After removing division 





To convert negative exponents to division operators, use the Remove Negative Powers command.
Remove Division 1 Level
Converts division to multiplication, as Remove Division does, but applies only to the first level of operators.
Selected expression 
After removing division 





To convert the first level of negative exponents into division operators, use the Remove Negative Powers 1 Level command.
Remove Negative Powers
Converts negative exponents to positive in a selected expression by replacing multiplication with division and division with multiplication.
Selected expression 
After removing negative powers 





Remove Negative Powers 1 Level
Converts negative exponents to positive, as Remove Negative Powers does, but applies only to the first level. If the selected expression has no negative exponents at the first level, this command has no effect.
Selected expression 
After removing negative powers 




(no effect) 
Number Crunch
Changes integers to floatingpoint numbers in a selected expression and then evaluates the expression.
Selected expression 
After number crunch 









Use the Show All Digits command to show up to 15 decimal places in a floatingpoint number.
Number Crunch displays NaN (Not a Number) for operations that result in undefined values. It displays Infinity for operations that result in a value too large to calculate. Small numbers can sometimes be evaluated to zero.
Selected expression 
After number crunch 





Show All Digits
Shows the full internal accuracy of a floatingpoint number.
Selected number 
After showing all digits 



Evaluate
Evaluates the selected expression. The operations performed depend on the type of expression selected, as shown in the following examples:
•Rewrites an expression raised to a power less than 20 as a product.
Selected expression 
After evaluating 



•Computes the factorial of an integer. If the result is too large to calculate, the result appears as Infinity.
Selected expression 
After evaluating 



•Computes the determinant of a 1by1 or 2by2 matrix.
Selected expression 
After evaluating 



•Extracts a term from a sum or product.
Selected expression 
After evaluating 



•Evaluates a substitution just as the Evaluate Substitution command does.
•Rewrites an Evaluate Between operator as a difference.
Selected expression 
After evaluating 



•Rewrites the logarithm of a product as a sum of logarithms and rewrites a logarithm of a power as a product.
Selected expression 
After evaluating 





•Rewrites a logarithm to a base in terms of natural logarithms.
Selected expression 
After evaluating 



•Rewrites a choice function in terms of factorials.
Selected expression 
After evaluating 



Evaluate Substitution
Performs a specified substitution and then simplifies the expression. When an Evaluate Between operator is selected, this command rewrites the expression as a difference.
Selected expression 
After evaluating 





Evaluate Integrals
Rewrites a selected integral with a polynomial integrand. This command converts a definite integral into an indefinite integral evaluated between the upper and lower bounds. Use Evaluate Integrals several times to integrate a polynomial fully.
Selected expression 

Evaluated once 

Evaluated twice 

Evaluate Derivatives
Evaluates a selected derivative, applying the chain rule to complex expressions when necessary. This command evaluates a partial derivative only when all dependencies are explicitly written.
This command treats elements in a total derivative as if they depended on the variable of differentiation. Use the Evaluate command to expand an nth derivative before using Evaluate Derivatives to evaluate it.
Before 
After 





Evaluate Derivatives 1 Level
Evaluates only the first level of a selected derivative.
Before 
After 



Use the Rules popup menu on the Functions page to store and apply rules that transform expressions.
For example, use Enter Rule to store a rule such as a = a + 3. Then use Apply Rule to substitute a + 3 for a in another expression.
Enter Rule
Stores a rule for substituting one expression for another. Select the expression you want to store as a rule before you choose Enter Rule. You can store only one rule at a time.
Designate Dummy
Designates a selected term to be a dummy variable. Use a dummy variable in a rule to substitute the expression on the right side of the rule for any variable, not just the variable explicitly named on the left. A dummy variable appears in boldface. For example, if you designate x in the rule x = a 2– as a dummy variable, you can substitute a 2– or x for any variable in an expression.
Select the term you want to be a dummy variable before you choose Designate Dummy. Then use the Apply Rule command to replace a selected expression with the expression assigned to the dummy variable.
Apply Rule
Substitutes one term or set of terms for another in a selected expression, using the rule stored with the Enter Rule command.
Rule entered 

Selected expression 

After rule is applied 

Before you apply a rule that contains a dummy variable, select the term you want the variable to replace. In the following example, x is the dummy variable in the rule.
Rule entered 

Before rule is applied 

After rule is applied 

Simplify
Simplifies the selected expression. To evaluate fractions that involve infinity or division by zero, use the Number Crunch command instead of Simplify.
The operations performed depend on the type of expression selected, as shown in the following examples:
•Performs integer arithmetic.
Selected expression 
After simplifying 







When the result is too large to calculate, it appears as Infinity.
•Groups terms in a sum or product.
Selected expression 
After simplifying 







•Divides out common factors in a fraction.
Selected expression 
After simplifying 





Use the Remove Negative Powers command to remove negative powers from the result.
•Interprets the complex number i, represented by the Greek letter iota .
Selected expression 
After simplifying 



•Distributes exponentiation across multiplication and division.
Selected expression 
After simplifying 





Simplifying x produces rather than .
Simplify Some
Simplifies the selected expression, as the Simplify command does, but does not multiply fractions.
Selected expression 
After simplifying 



Isolate Term
Isolates a selected expression on one side of the equal sign. This command does not combine terms or solve for the selected expression.
Selected expression 
After isolating term 







Expand First Term
Expands the first term of a selected summation or product.
Selected expression 
After expanding 





Expand All Terms
Expands all terms of a selected summation or product.
Selected expression 
After expanding 




