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.
Excellent!
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 +
)
Good work!
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 can start by distributing \(-8\) to both terms inside the parentheses. Here is how it goes step by step:

1. Rewrite the expression: \[ 18 - 8(3x - 8) = 18 + (-8(3x - 8)) \]

2. Distribute \(-8\): \[ -8(3x - 8) = -8 \cdot 3x + (-8) \cdot (-8) \] This simplifies to: \[ -24x + 64 \]

3. Combine it back into the expression: \[ 18 + (-24x + 64) \]

4. Combine the constant terms (18 and 64): \[ 18 + 64 = 82 \]

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

In summary: \[ 18 - 8(3x - 8) = 82 - 24x \]