TopPolynomials are expressions which consist of variables with exponents and constants. This exponent can be of any degree. These Polynomials are used frequently in Trigonometry, calculus, algebra etc. There is a rule in polynomials that they can contain constant, variables, exponents and operations like addition, subtraction, multiplication but they cannot have any kind of division in expression. One more thing is to be remembered that polynomials cannot contain Radicals, infinite terms or any kind of negative exponent. Now let us see how to determine if a polynomial is the difference of two squares.
Let us understand it step by step by taking an example:
Step 1: First of all we have to simplify the given expression. For example: Assume that we are given a polynomial expression 2x2 + 2x2 - 10 – 6. Now we have to simplify it as 4x2 – 16.
Step 2: Examine the Integer value in equation. The integer in equation is a perfect Square. In this equation integer term is 16 which is a perfect square. If it is possible to write it in terms of exponent then we will write it. Here we can write 16 in terms of exponent as 42.
Step 3: Now we will review the equation and will check that if it is making a difference of two perfect square terms which means that this equation is representing a subtraction of two perfect square terms. Now we will Set this equation in format of subtraction of two square terms that is a2 – b2.
Step 4: Now we will factorize this equation using the difference of two square formula that is (a + b)(a - b). Equation 4x2 – 16 will be written in factorized form as (2x + 4)(2x - 4).