Multiply monomials by polynomials

 is an exercise under the Algebra II Math Mission. This exercise practices using the distributive property to express the product of a monomial and a polynomial as a single polynomial.

Types of Problems
There are two types of problem in this exercise:
 * 1) Express the product of in standard trinomial form: This problem has a binomial and students are asked to express the product of it as standard trinomial form. Distributive property can be used to speed up this process.
 * 2) Find the area of the rectangle: This problem has the length of one side of a rectangle expressed as a polynomial. Students are expected to find the area of the rectangle and express it as a trinomial.

Strategies
Knowledge of generating input and output pairs of a function are recommended for success on this exercise.
 * 1) In order to find the product of two polynomials, user must multiply each term in first polynomial by each term in the second polynomial. User can view this process as a double application of the distributive property.
 * 2) The expression on the left-hand side of the equation is a product of two binomials. User can replace the two terms with their product and obtain an equivalent equation (which means it will have the same solutions).

Real-life Applications

 * 1) Polynomials can be used via power series to represent many complicated functions and calculus is simpler to perform on polynomials than other functions. Thus any comfort with polynomials should increase calculus ability.
 * 2) Factoring polynomials is an important skill in solving inequalities and equations with polynomials.
 * 3) Factoring polynomials can be used for solving equations with polynomials, such as those that appear in many business models.