2. Multiplication of polynomials

We studied that algebraic terms are either variable or numbers or a single number and variables multiplied together.

 

Each terms in an algebraic expression are separated by the arithmetic operations addition or subtraction.

 

The algebraic expression can be a single term or double term or more than two terms.

 

An algebraic expression with one or more than one terms is called a polynomial.

The polynomials are classified based on the number of terms as follows:

1. Monomial :

Example: \(5x^2\), \(6x\).

 

2. Binomial:

Example: \(a + 3\), \(x^2 + 4\).

 

3. Trinomial:

Example: \(x^2 + 5x + 2\), \(s + t + 3\).
If we have \(2\) polynomials with variables and numbers, then the product is the result of (product of coefficients of polynomials) \(×\) (product of variables of polynomials).

To multiply polynomials of higher degrees, find the product of coefficients of polynomials and then use the law of exponents to add the power of similar variables.

The useful law of exponents are as follows:

1. $a^m\times a^n=a^{m+n}$ 

2. ${\left(a^m\right)}^n=a^{\mathit{mn}}$