Using the Distributive Property
Apply the distributive property in Grade 9 algebra to multiply a factor across parentheses. Expand expressions like a(b+c) = ab+ac and simplify polynomial equations.
Key Concepts
Property When substituting an expression for a variable with a coefficient, the coefficient must be distributed to every term inside the parentheses. For example, in $5x 2y = 1$, if $y = ( 2x 4)$, the equation becomes $5x 2( 2x 4) = 1$. Explanation Think of the number outside the parentheses as a party host! It must greet every single guest inside. When you substitute an expression, the coefficient outside must be multiplied by every term inside—no exceptions. Don't let anyone get left out, not even the negative signs who are just a bit shy and hiding in the back! Examples In the expression $12( 2y + 11)$, distribute the $12$ to get $12( 2y) + 12(11) = 24y + 132$. Be careful with negatives! In $5x 2( 3x + 4) = 1$, distributing the $ 2$ correctly gives $5x + 6x 8 = 1$. After substituting $x = 3y + 9$ into $10x 5y = 10$, you get $10( 3y + 9) 5y = 10$.
Common Questions
What is the distributive property in algebra?
The distributive property states that a(b + c) = ab + ac. Multiply the factor outside parentheses by each term inside, then combine the results.
How do you use the distributive property to solve equations?
Multiply the outside factor by each term in parentheses to remove them, combine like terms, then solve using inverse operations.
What common mistakes should students avoid with the distributive property?
A common mistake is only multiplying the first term inside parentheses. Remember to distribute to every term inside, including those preceded by negative signs.