M6|L21 Combining Like Terms (Part 2)Sign out

Question

Write equivalent expressions.
How could you start to write equivalent expressions?
18 − 8(3x − 8)

Start left to right and subtract 18 − 8 first.

Use the distributive property to distribute the -8 to the values within the parentheses.

Answer 1

To write equivalent expressions for the given expression \( 18 - 8(3x - 8) \), you can apply the distributive property. Here’s how to do it step by step:

1. Distribute the -8: Multiply -8 by each term inside the parentheses:

   \[ -8(3x) + -8(-8) \]

   This simplifies to:

   \[ -24x + 64 \]

2. Combine with the constant: Now, incorporate the constant 18 from the original expression:

   \[ 18 - 24x + 64 \]

3. Combine like terms: Combine the constants (18 and 64):

   \[ 82 - 24x \]

Thus, the equivalent expression for \( 18 - 8(3x - 8) \) is:

\[ 82 - 24x \]

This process shows how you can systematically apply the distributive property and combine like terms to generate an equivalent expression.