LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

MULTIPLICATION OF MONOMIAL WITH POLYNOMIAL

__MULTIPLICATION OF ALGEBRAIC EXPRESSION OF MONOMIAL WITH POLYNOMIAL -__

**Multiplying a monomial (single-term algebraic expression) with a polynomial (multi-term algebraic expression) follows the distributive property. You need to distribute the monomial to each term of the polynomial. Here are the steps to do it:**

__Identify the monomial and the polynomial:-__The monomial is the single term that you want to multiply with the polynomial.The polynomial is the expression consisting of multiple terms.__Multiply the monomial with each term in the polynomial:-__For each term in the polynomial, multiply it by the monomial.You will effectively distribute the monomial to each term. Multiply the monomial by each term in the polynomial.__Combine like terms:-__After multiplying the monomial with each term in the polynomial, look for like terms (terms with the same variable bases) and combine them by adding or subtracting their coefficients.

**Here's an example to illustrate this process:**

**Example.1) Multiply 3x (monomial) by the polynomial 2x²+ 5x - 1.**

**Ans.)**

__Distribute the monomial to each term of the polynomial:-__3x * 2x² = 6x³ (multiply coefficients and add exponents) 3x * 5x = 15x² (multiply coefficients and add exponents) 3x * (-1) = -3x (multiply coefficient by the constant)__Combine like terms:-__In this case, there are no like terms to combine because each term in the polynomial is different.

**So, the result of multiplying 3x by the polynomial 2x²+ 5x - 1 is 6x³+ 15x²- 3x. (Ans.)**

**Example.2) Multiply the monomial 2x with the polynomial 3x²+ 4x - 1.**

**Ans.)**

__Identify the monomial and the polynomial:-__

** Monomial:- 2x**

** Polynomial:- 3x²+ 4x - 1**

** 2. Multiply the monomial with each term in the polynomial:- **

** Multiply 2x by 3x²:- (2x) * (3x²) = 6x³**

** Multiply 2x by 4x:- (2x) * (4x) = 8x²**

** Multiply 2x by -1:- (2x) * (-1) = -2x**

** 3. Combine like terms:- **

** There are no like terms in this case because each term in the polynomial has a different variable base.**

**So, the result of multiplying 2x with 3x²+ 4x - 1 is 6x³+ 8x²- 2x. (Ans.)**