Products
This Grade 6 algebra skill from Yoshiwara Elementary Algebra covers the multiplication of algebraic expressions (products). Students learn to multiply monomials, binomials using FOIL, and polynomials, applying the distributive property and combining like terms to produce simplified products.
Key Concepts
Property To simplify a product such as $3(2a)$, we multiply the numerical factors to find $3(2a) = (3 \cdot 2)a = 6a$. This calculation is an application of the associative law for multiplication. We can see why the product is reasonable by recalling that multiplication is repeated addition, so that $3(2a) = 2a + 2a + 2a = 6a$.
Examples To simplify $4(5b)$, you multiply the numerical factors: $(4 \cdot 5)b = 20b$. To simplify $ 6(2y)$, you multiply the numbers: $( 6 \cdot 2)y = 12y$. To simplify $ 3( 8z)$, you multiply the coefficients: $( 3 \cdot 8)z = 24z$.
Explanation When a number is outside parentheses with a single term inside, just multiply the numbers together. Think of it as a shortcut for adding the term multiple times. It's all about grouping the numbers first to simplify.
Common Questions
How do you multiply two monomials?
Multiply the coefficients and add the exponents of like variables. For example, (3x^2)(4x^3) = 12x^5.
What is the FOIL method?
FOIL stands for First, Outer, Inner, Last—a method for multiplying two binomials. Multiply each pair of terms and combine like terms.
How do you multiply a binomial by a trinomial?
Distribute each term of the binomial to each term of the trinomial (6 products total), then combine like terms.
What is an example of a product in algebra?
(x + 2)(x + 3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6, using FOIL or the distributive property.
Where are products in algebra taught?
Algebraic products are covered in the Yoshiwara Elementary Algebra textbook for Grade 6.