Find the Product 2(9x-2y)
The question provides an algebraic expression and asks for the product of 2 and the binomial expression (9x - 2y). This requires using the distributive property to multiply each term in the parenthesis by 2, which would result in a new algebraic expression. The question is asking for this multiplication to be carried out to obtain a simplified expression representing the product.
$2 \left(\right. 9 x - 2 y \left.\right)$
Answer
Solution:
Step 1:
Utilize the distributive property to expand the expression: $2 \times (9x) + 2 \times (-2y)$.
Step 2:
Perform the multiplication.
Step 2.1:
Calculate $2 \times 9$ to get $18x$. The expression now is $18x + 2 \times (-2y)$.
Step 2.2:
Calculate $2 \times -2$ to obtain $-4y$. The final expression is $18x - 4y$.
Knowledge Notes:
The distributive property is a fundamental algebraic property used to simplify expressions and perform multiplication over addition or subtraction within parentheses. It states that for any three numbers, variables, or expressions \(a\), \(b\), and \(c\), the following is true:
\[ a(b + c) = ab + ac \] \[ a(b - c) = ab - ac \]
In the context of the given problem, the distributive property is applied to the expression \(2(9x - 2y)\), which involves multiplying \(2\) by each term inside the parentheses.
The multiplication step is straightforward arithmetic. It requires multiplying the coefficient outside the parentheses by each term inside the parentheses. In this case, \(2\) is multiplied by \(9x\) and \(-2y\) respectively.
The final expression \(18x - 4y\) is the simplified form of the original expression, with the distributive property applied and the multiplication carried out. This is the product of the given expression.
