Find special products of binomials (basic)

The  exercise appears under the Algebra basics Math Mission. This exercise practices finding perfect squares of the forms $$(x+a)^2$$ and $$(x-a)^2$$, and differences of squares of the form $$(x+a)(x-a)$$.

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


 * 1) Find the values for integers $$k$$ and $$m$$ that makes the following equation true.: This problem involves a binomial expression with variables for integers $$k$$ and $$m$$. The student is expected to find the values of  $$k$$ and $$m$$ that make the equations true. 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) Students are asked to find the values of $$k$$ and $$m$$ that would make the equation true. They can start by expressing the product on the left-hand side of the equation in standard quadratic form. Then they can compare the two quadratic expressions on each side of the equation by matching the coefficients of terms that are alike.

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.