Question

Use the Distributive Property to write equivalent expressions for 4(4x + 3y).

Answer 1

To use the Distributive Property on the expression 4(4x + 3y), multiply 4 by each term inside the parentheses to get 16x + 12y, which is the simplified equivalent expression.

Step-by-step explanation:

Using the Distributive Property

The Distributive Property states that for any numbers a, b, and c, the expression a(b + c) is equivalent to ab + ac. To apply the Distributive Property to the expression 4(4x + 3y), we multiply the number outside the parentheses, which is 4, by each term inside the parentheses. Therefore, we get:

• 4 × 4x = 16x
• 4 × 3y = 12y

Putting it all together, the equivalent expression using the Distributive Property is 16x + 12y.

This process of distribution simplifies the expression and allows us to perform further operations if necessary. It is a foundational concept in algebra that facilitates the manipulation of equations.