Factor perfect squares

The  exercise appears under the Algebra I Math Mission. This exercise practices factoring quadratic expressions of the general perfect square forms: $$(ax)^2+2abx+b^2$$ or $$(ax)^2-2abx+b^2$$. The factored expressions have the general forms $$(ax+b)^2$$ or $$(ax-b)^2$$.

Types of Problems
There are two types of problem in this exercise:
 * 1) Factor the polynomial expression completely: This problem involves a polynomial expression including squares and students are asked to factor it completely. The answer is to be typed in the text box below.
 * 2) Find the value of both variables: This problem also has a quadratic equation that is a perfect square and can as $$(x+d)^2$$ or $$(x-d)^2$$ 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 difference of squares factoring technique is highly recommended for accuracy and efficiency on this exercise.


 * 1) The difference of squares formula says $$ a^2-b^2=(a+b)(a-b)$$.
 * 2) All expressions are monic (have leading coefficient of one) so the square of the constant will be the second space and $$x$$ will always be in the first space.
 * 3) The answer box will automatically insert a closing parentheses when the user inputs a beginning parentheses.

Real-life applications

 * 1) Square roots have many uses in the physics as they are the way to undo squares in famous formulas like $$E=mc^2$$.
 * 2) Applications to trigonometry are also evident since the right triangle trigonometry is based on the Pythagorean Theorem.
 * 3) In geometry, the square root is necessary to find the distance between points or the magnitude of a vector.