Multiply binomials by binomials

The  exercise appears under the Algebra basics Math Mission and Algebra I Math Mission. This exercise practices using the distributive property to express the product of two binomials as a single polynomial.

Types of Problems
There is one type of problem in this exercise:


 * 1) Multiply the binomials and express the product in standard quadratic form: This problem involves two binomials. The student is expected to multiply the binomials then type the product in the text box in standard quadratic form.Multiply binomials by binomials.PNG

Strategies
Knowledge of the distributive property is required to complete this exercise. There are other techniques such as the FOIL technique that can help to make it more efficient.
 * 1) To multiply binomials it is possible to use the FOIL technique which involves finding the product of the first terms in each binomials, then the outer, then the inner, and finally the last. In this problem the outers and inners will need to be combined.
 * 2) All of the binomials used in this exercise are monic, that is, their leading coefficient is one.
 * 3) The sum of the constants is the coefficient to the $$x$$, and the product of these is the constant.
 * 4) The answer choice "none of the above" is employed regularly.

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.