# Intro: Algebra Interaction

The three core principles of the algebra interaction are:

AlgebraKiT automatically simplifies an expression.

The default task when creating an algebra interaction is set to Simplify. With this task selected, AlgebraKiT automatically simplifies the given expressen.

##### Example

With a task $4+5$, AlgebraKiT will evaluate the sum, because $9$ is a simpler expression than $4+5$.

Try it yourself:

• $2x+4x+4$
AlgebraKiT will combine the like terms.
• $x(x+1)$
AlgebraKiT will do nothing. Expanding the brackets is not necessarily ‘simpler’.
• $x(x+1)-x^2$
Now AlgebraKiT will expand the brackets, because it can then cancel terms and reach a simple result.
• $\frac{2x+4}{x^2+2x}$
Using the mathematical knowledge that AlgebraKiT has, it decides to factor both numerator and denominator and cancel factors to reach a simpler result.

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The interaction tasks indicate what the student should do.

An important principle in AlgebraKiT is that an author does not specify the answer, but the problem. This allows AlgebraKiT to evaluate intermediate steps and support the student with the derivation.

You can use the dropdown elements to choose from the available tasks.

Try it yourself:

• Solve $2(2x+5)=5-x$
• Expand $x(x+1)$
• Factor $4x^2+12x$
• Write $184300$ into scientific notation.
You can use audience and modes to influence how AlgebraKiT solves the problem.

#### Audience

The audience defines the type of student for which the exercise was meant. It influences what mathematical steps are available and how expressions are written.

##### Note

In a low-level audience such as Arithmetic, AlgebraKiT will not be able to solve more advanced problems, like equations.

#### Modes

##### Examples

AlgebraKiT will interpret $\sin{30}$ by default as the sine of 30 radians. To use degrees, you can set mode gonio_degrees.

To force AlgebraKiT (and the student) to write the fraction $\frac{10}{8}$ into the mixed fraction 1¼,  set mode nf_rational.

AlgebraKiT will solve the equation $x^2+5x+6=0$ by default by factoring. To force use of the Quadratic Formula (‘abc-formula’), set mode solve_quadratic_abc.