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.
You got it!
Rewriting subtraction using addition can be helpful to keep track of the subtraction symbol when distributing. Start by rewriting this expression using addition.
18 − 8(3x − 8)

= 18 +
(3x +
)
Excellent!
Use the distributive property to write an equivalent expression.
18 - 8(3x - 8)

= 18 + −8(3x + -8)

= 18 + (
·
) + (
·
)

Answer 1

To rewrite the expression \(18 - 8(3x - 8)\) using the distributive property, we first need to distribute the \(-8\) across the terms within the parentheses.

We can rewrite the expression as follows:

1. Rewrite subtraction as addition: \[ 18 - 8(3x - 8) = 18 + (-8)(3x - 8) \]

2. Now distribute \(-8\) to each term inside the parentheses: \[ -8(3x) + -8(-8) = -24x + 64 \]

3. Now, combine these terms back into the original expression: \[ 18 + (-24x + 64) \]

4. Finally, combine the constant terms \(18 + 64\): \[ 18 + 64 = 82 \]

So, the equivalent expression is: \[ -24x + 82 \]

To fill in the blanks provided: \[ = 18 + (-8)(3x + 8) \] Continuing the next steps gives: \[ = 18 + (-24x) + 64 \]

Thus, your final equivalent expression is: \[ -24x + 82 \]