Math  /  Algebra

Question1 2 3 6 7 a 9. 1穓
Which expression is equivalent to (xy)z(x y) z ? (x+y)+z(x+y)+z 2z(xy)2 z(x y) x(yz)x(y z)

Studdy Solution

STEP 1

What is this asking? Which expression is the same as (xy)z(x y) z? Watch out! Don't get tricked by the plus signs or the number 22!
We're dealing with multiplication here, and order doesn't matter when everything is multiplied!

STEP 2

1. Understand the Associative Property
2. Apply the Associative Property
3. Identify the Equivalent Expression

STEP 3

The *associative property of multiplication* tells us that when we multiply a bunch of numbers together, it doesn't matter how we group them with parentheses!
It's like a multiplication party where everyone gets to mingle!

STEP 4

For example, if we have (23)4(2 \cdot 3) \cdot 4, we can calculate it as (6)4=24(6) \cdot 4 = 24.
But, we could also group it as 2(34)=2(12)=242 \cdot (3 \cdot 4) = 2 \cdot (12) = 24.
See? Same answer!

STEP 5

Our problem has (xy)z(x y) z, which means we multiply xx and yy first, and *then* multiply by zz.

STEP 6

Using the associative property, we can regroup the expression as x(yz)x(y z).
This means we multiply yy and zz first, and *then* multiply by xx.

STEP 7

We're looking for an expression that's the same as (xy)z(x y) z, and we know from the associative property that this is the same as x(yz)x(y z).

STEP 8

Let's look at our choices: (x+y)+z(x+y)+z Nope, this has addition, not just multiplication! 2z(xy)2 z(x y) This one has an extra 22 being multiplied, so it's not the same. x(yz)x(y z) This is exactly what we got when we applied the associative property!

STEP 9

The expression x(yz)x(y z) is equivalent to (xy)z(x y) z.

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