Question

Prove z + z + z + z = 4z. Replace each step with the correct equivalent expression based on the given property or operation. Drag the correct tiles to show the steps in order. z + z + z + z = Step 1 (Multiplicative Identity Property) = Step 2 (Distributive Property) = Step 3 (Addition) = Step 4 (Commutative Property of Multiplication) z • 4 1 + (z • z • z • z) 4z z • 0 + z • 0 + z • 0 + z • 0 z • 1 + z • 1 + z • 1 + z • 1 z • (1 + 1 + 1 + 1) ↓ ↓ ↓

Answer 1

Step 1:
`z*1+z*1+z*1+z*1=`

Step 2:
`z(1+1+1+1)=`

Step 3:
`z*4=`

Step 4:
`z*4 = 4z`

Explanation:

Given

`z+z+z+z = 4z`

Required

Match the steps with equivalent properties

Step 1: Multiplicative Identity Property

This states that:

`x = 1 * x`

So, the expression becomes:

`z*1+z*1+z*1+z*1=`

Step 2: Distributive Property

This states that:

`ab + bc = b(a+c)`

So, the expression becomes

`z*1+z*1+z*1+z*1=`

`z(1+1+1+1)=`

Step 3: Addition

Here, we simply add the expressions in the bracket

`z(1+1+1+1)=`

`z(4) =`

`z*4=`

Step 4: Commutative Property of Multiplication

This states that:

`ab=ba`

So, we have:

`z*4=`

`z*4 = 4*z`

`z*4 = 4z`