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

Answer:

Step 1: $z*1+z*1+z*1+z*1=$

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

Step 3: $z*4=$

Step 4: $z*4 = 4z$

Step-by-step 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:

$z*4=$

$z*4 = 4*z$

$z*4 = 4z$