The Distributive Law
The Distributive Law states that multiplication distributes over addition: a(b + c) = ab + ac. Covered in Yoshiwara Elementary Algebra Chapter 4: Applications of Linear Equations, this law is one of the most frequently used algebraic rules for Grade 6 students when simplifying expressions, solving equations, and working with polynomials. When the terms inside parentheses are not like terms, the distributive law is the only way to simplify the expression.
Key Concepts
Property If $a$, $b$, and $c$ are any numbers, then $$a(b + c) = ab + ac$$ If the terms inside parentheses are not like terms, we have no choice but to use the distributive law to simplify the expression.
Examples To simplify $5(x+4)$, distribute the 5 to each term: $5(x) + 5(4) = 5x + 20$. To simplify $ 3(2y 1)$, multiply each inner term by $ 3$: $ 3(2y) 3( 1) = 6y + 3$. To simplify $(a 5)6$, distribute the 6 from the right: $a(6) 5(6) = 6a 30$.
Explanation The distributive law lets you multiply a number outside parentheses by each term inside. It's like sharing the outside number with every term in the group through multiplication. This is essential when you can't combine the terms inside first.
Common Questions
What is the distributive law?
The distributive law states that a(b + c) = ab + ac. You multiply the factor outside the parentheses by each term inside.
How do you apply the distributive law?
Multiply the outside factor by the first term, then by the second term (and any additional terms), and write all the resulting products added together.
When must you use the distributive law?
Whenever you have a factor multiplying a sum or difference in parentheses. If the terms inside are unlike, you must distribute — you cannot combine them first.
Where is the distributive law in Yoshiwara Elementary Algebra?
It is featured in Chapter 4: Applications of Linear Equations of Yoshiwara Elementary Algebra.
Does the distributive law work for subtraction too?
Yes. a(b - c) = ab - ac. The sign of each term inside is preserved after distribution.