Multiplying Monomials
Multiplying Monomials teaches Grade 6 students how to multiply single-term expressions by rearranging factors to group numerical coefficients and apply the first law of exponents (a^m × a^n = a^(m+n)) to each shared base. This skill is taught in Yoshiwara Elementary Algebra Chapter 7: Polynomials and is the building block for multiplying polynomials of all types. Students practice simplifying expressions like (3x²)(5x³) = 15x⁵ by multiplying coefficients and adding exponents.
Key Concepts
Property To multiply two monomials, rearrange the factors to group together the numerical coefficients and the powers of each base. Then, multiply the coefficients and use the first law of exponents for the variable factors.
Examples To multiply $(3a^2b)(4a^3b^4)$, we group and multiply: $(3 \cdot 4)(a^2 \cdot a^3)(b \cdot b^4) = 12a^5b^5$.
The product of $( 6x^3y^2)(2x^5y)$ is found by multiplying coefficients and adding exponents of like bases: $( 6 \cdot 2)(x^3 \cdot x^5)(y^2 \cdot y) = 12x^8y^3$.
Common Questions
How do you multiply two monomials?
Multiply the numerical coefficients together and use the first exponent law to combine powers of the same base (add the exponents). For example, (3x²)(5x³) = 15x⁵.
What is a monomial?
A monomial is a single-term expression consisting of a number, a variable, or a product of numbers and variables with whole number exponents. Examples: 5, x², 3xy².
What rule do you use for the variables when multiplying monomials?
Use the product rule for exponents: a^m × a^n = a^(m+n). Add the exponents of matching variables.
Where is multiplying monomials in Yoshiwara Elementary Algebra?
It is covered in Chapter 7: Polynomials of Yoshiwara Elementary Algebra.
How does multiplying monomials extend to multiplying polynomials?
Multiplying a polynomial by a monomial uses the same rules — distribute the monomial to each term of the polynomial and apply the product rule to each variable.