Multiplying a Monomial by a Polynomial
In this lesson, we will learn how to multiply a monomial (a single term expression) by a polynomial (an expression with multiple terms). This skill is fundamental in algebra and uses the distributive property.
Key Definitions
Monomial: An algebraic expression consisting of only ONE term.
Examples:
Examples:
3x, -5a², 2xy, 7
Polynomial: An algebraic expression consisting of TWO or MORE terms.
Examples:
Examples:
x + 2, 3a² - 5a + 1, x² - y²
Distributive Property:
a(b + c) = ab + ac
The monomial multiplies EACH term of the polynomial!
Visual Representation
Step-by-Step Procedure
1
Multiply the monomial by the first term of the polynomial
2
Multiply the monomial by the second term of the polynomial
3
Continue for all remaining terms
4
Write all products as a sum (keep the signs!)
5
Simplify by combining like terms if needed
General Rule:
a(b + c + d) = ab + ac + ad