Operations on Types of Polynomials

Multiplication of Monomials

Example: Multiply 4a and 3ba³?

Solution: 

First we need to group Coefficients and Variables

(4 * 3) (a * a³) (b)

Apply exponential law,

12a¹⁺³b

12a⁴b

Multiplication of three or more monomials

Example: Multiply a², 2ab³, 4ab?

Solution: 

(4 * 2) (a² * a * a) (b³ * b)

8a⁴b⁴

Multiplication of monomial by binomial

Example: Multiply 2a by a + 4?

Solution: 

(2a * a) + (2a * 4)

2a² + 8a

Multiplication of monomial by trinomial 

Example: Multiply 3a by 2a² + 3ab + 4?

Solution: 

(3a * 2a²) + (3a * 3ab) + (3a * 4)

6a³ + 9a²b + 12a

Multiplication of Binomial by a Binomial

Example: Multiply 4a + 3 and 2a +1?

Solution: 

4a (2a + 1) + 3 (2a + 1)  [ now its like multiplication of monomial and binomial ]

8a² + 4a + 6a + 3

8a² + 10a + 3

Multiplication of Binomial and Trinomial 

Example: Multiply 4a + 1 and a² + 2a + 1?

Solution: 

4a (a² + 2a + 1) + 1 (a² + 2a + 1)

4a² + 8a + 4a + a² + 2a + 1

5a² + 14a + 1

Multiplication of Polynomial and Monomial 

Example: Multiply a³ + a² + a + b + 3 and 4a?

Solution: 

(4a * a³) + (a² * 4a) + (a * 4a) + (b * 4a) + (3 * 4a)

4a⁴ + 4a³ + 4a² + 4ab + 12a

Multiplication of Polynomial and Polynomial

Example: Multiply 2x⁴ + 3x⁵ + 4 and 2x + 1?

Solution: 

(2x⁴ * 2x) + (3x⁵ * 2x) + (4 * 2x) + (2x⁴ * 1) + (3x⁵ * 1) + (4 * 1)

2x⁵ + 6x⁶ + 8x + 2x⁴ + 3x⁵ + 4

6x⁶ + 5x⁵ + 2x⁴ + 8x + 4

Types of Polynomials: In mathematics, an algebraic expression is an expression built up from integer constants, variables, and algebraic operations. There are mainly four types of polynomials based on degree-constant polynomial (zero degree), linear polynomial ( 1st degree), quadratic polynomial (2nd degree), and cubic polynomial (3rd degree).

There are 3 types of polynomials based on the number of terms in the polynomial – monomial, binomial, and trinomial, and for more than that we use the general term polynomial. This article is about the types of polynomials – Monomials, Binomials, and Polynomials in detail.