# CLASS-6MULTIPLICATION 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:

1. 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.
2. 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.
3. 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.)

1. 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)
2. 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.)

1. 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.)  