Question

What are the special products of polynomials?

Answer 1

Hint: To solve this question first we need to know the concept of polynomial a polynomial is basically an expression which consists of variables and coefficients which involves certain operations like addition subtraction multiplication there are many types of polynomials which includes monomial, binomial, trinomial etc.

Complete step by step solution:
The question asks us to write about the special products of polynomials. There are many special products of polynomials to ease the arithmetic operation like multiplication, addition, subtraction and division.
1) The first formula in that context is squaring of the term where the function is the binomial as shown below: When we multiply two linear (degree of 1) binomials, we create a quadratic (degree of 2) polynomial with four terms. The middle terms are like terms so we can combine them and simplify to get a quadratic or 2nd degree trinomial (polynomial with three terms). There are some special products of binomials that make finding simplifying expressions and equations easier.
$\Rightarrow {{\left( a+b \right)}^{2}}=\left( a+b \right)\left( a+b \right)={{a}^{2}}+2ab+{{b}^{2}}$
Here $a$ and $b$ are the two functions which are multiplied to each other.
2) The second formula is the cube of the function. When we multiply three linear (degree of 1) binomials, we create a cubic (degree of 3) polynomial with more than three terms. There are some terms which are like terms so we can combine them and simplify to get a quadrinomial or a $4$ degree polynomial. The above written part could be formulated as:
$\Rightarrow {{\left( a+b \right)}^{3}}=\left( a+b \right)\left( a+b \right)\left( a+b \right)={{a}^{3}}+{{b}^{3}}+3ab\left( a+b \right)$

Note: There are many other special formulas for the polynomials. Polynomials are major of three types namely monomial, binomial, trinomial which means that the function has $1$ , $2$ and $3$ terms respectively.