8(4y) as Associative Property of multiplication

To express \( 8(4y) \) using the **Associative Property** of multiplication, we rearrange the grouping of numbers without changing their product. The **Associative Property** states that for any three numbers \( a \), \( b \), and \( c \):

\[
a \times (b \times c) = (a \times b) \times c
\]

Now, let's apply this to \( 8(4y) \):

\[
8 \times (4 \times y) = (8 \times 4) \times y
\]

\[
= 32 \times y
\]

Thus, using the Associative Property of multiplication, \( 8(4y) \) can be rewritten as \( (8 \times 4) \times y = 32y \).

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. Can the Distributive Property be applied to \( 8(4y) \)?
2. What is the Commutative Property of multiplication, and how does it differ from the Associative Property?
3. How would you simplify an expression like \( 3(2x + 5) \) using the Associative Property?
4. What is the Associative Property of addition, and how is it similar to multiplication?
5. How do these properties help in solving complex algebraic expressions?

**Tip:** The Associative Property allows you to regroup terms, which is especially useful when simplifying expressions with multiple variables or constants.

Learn how to simplify the expression 8(4y) using the Associative Property of Multiplication. This guide covers key algebraic concepts like the Associative Property and demonstrates how to rearrange and simplify terms effectively. Suitable for students in Grades 6-8.

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