Section 1
Multiplying by a monomial
Property
To multiply a polynomial by a monomial, we use the distributive law. This means we multiply each term of the polynomial by the monomial.
Examples
- To multiply , distribute to each term: .
In this Grade 4 lesson from AoPS: Introduction to Algebra, students learn how to apply the distributive property and factoring with multiple variables, extending the same techniques used with single variables and constants. Through real-world problems involving baseball and football team rosters, students practice expanding expressions like 7(2x + 4y) = 14x + 28y and simplifying multi-variable expressions by distributing subtraction across parentheses. This lesson builds fluency with core algebraic manipulation skills essential for AMC 8 and AMC 10 competition math.
Section 1
Multiplying by a monomial
To multiply a polynomial by a monomial, we use the distributive law. This means we multiply each term of the polynomial by the monomial.
Section 2
Factor out the GCF
We use the Distributive Property in reverse to factor a polynomial. Find the GCF of all the terms and write the polynomial as a product.
Distributive Property:
If , , and are real numbers, then and . The form on the right is used to factor.
To factor the GCF from a polynomial:
Step 1. Find the GCF of all terms.
Step 2. Rewrite each term as a product using the GCF.
Step 3. Use the “reverse” Distributive Property to factor the expression.
Step 4. Check by multiplying the factors.
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Section 1
Multiplying by a monomial
To multiply a polynomial by a monomial, we use the distributive law. This means we multiply each term of the polynomial by the monomial.
Section 2
Factor out the GCF
We use the Distributive Property in reverse to factor a polynomial. Find the GCF of all the terms and write the polynomial as a product.
Distributive Property:
If , , and are real numbers, then and . The form on the right is used to factor.
To factor the GCF from a polynomial:
Step 1. Find the GCF of all terms.
Step 2. Rewrite each term as a product using the GCF.
Step 3. Use the “reverse” Distributive Property to factor the expression.
Step 4. Check by multiplying the factors.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter