Multiplying by a monomial
This Grade 6 algebra skill from Yoshiwara Elementary Algebra teaches students to multiply a polynomial by a monomial. Students apply the distributive property to multiply the monomial by each term of the polynomial, combining the results into a simplified polynomial expression.
Key Concepts
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.
$$a(b + c) = ab + ac$$.
Examples To multiply $4x(2x^2 5x + 3)$, distribute $4x$ to each term: $4x(2x^2) + 4x( 5x) + 4x(3) = 8x^3 20x^2 + 12x$.
Common Questions
How do you multiply a monomial by a polynomial?
Use the distributive property: multiply the monomial by each term of the polynomial. For example, 3x(2x^2 + 5x - 1) = 6x^3 + 15x^2 - 3x.
What is the distributive property?
The distributive property states a(b + c) = ab + ac. It allows you to multiply each term inside parentheses by the factor outside.
How do you handle exponents when multiplying a monomial by a polynomial?
Use the product rule: when multiplying powers with the same base, add the exponents. For example, x^2 x x^3 = x^5.
Can the monomial be a fraction or negative?
Yes. The process is the same: distribute the monomial (including its sign) to each term. A negative monomial will reverse signs.
Where is multiplying by a monomial taught?
Multiplying by a monomial is covered in the Yoshiwara Elementary Algebra textbook for Grade 6.