Factor simple special products

 is an exercise under the Algebra I Math Mission. This exercise practices factoring factoring quadratic expressions into the special products of the general forms $$(x+a)^2$$, $$(x-a)^2$$, and $$(x+a)(x-a)$$.

Types of Problems
There are two types of problem in this exercise:
 * 1) Find the two possible values: This problem has a quadratic equation where $$c$$ and $$d$$ are both integers. Students are expected to type one or two possible solutions for the equation.
 * 2) Find the value of both variables: This problem also has a quadratic equation that is a perfect square and can as $$(x+d)^2$$ where $$c$$ and $$d$$ are both positive integers. User is asked to find the value of both $$c$$ and $$d$$ that would make the equation true.

Strategies
Knowledge of the distributive property and factoring quadratics are recommended for success on this exercise.
 * 1) Student's goal is to find the values of $$c$$ and $$d$$ that will make the following equation true.
 * 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.