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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) ↓ ↓ ↓

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MrRoyal

Answer:

Step 1: [tex]z*1+z*1+z*1+z*1=[/tex]

Step 2: [tex]z(1+1+1+1)=[/tex]

Step 3: [tex]z*4=[/tex]

Step 4: [tex]z*4 = 4z[/tex]

Step-by-step explanation:

Given

[tex]z+z+z+z = 4z[/tex]

Required

Match the steps with equivalent properties

Step 1: Multiplicative Identity Property

This states that:

[tex]x = 1 * x[/tex]

So, the expression becomes:

[tex]z*1+z*1+z*1+z*1=[/tex]

Step 2: Distributive Property

This states that:

[tex]ab + bc = b(a+c)[/tex]

So, the expression becomes

[tex]z*1+z*1+z*1+z*1=[/tex]

[tex]z(1+1+1+1)=[/tex]

Step 3: Addition

Here, we simply add the expressions in the bracket

[tex]z(1+1+1+1)=[/tex]

[tex]z(4) =[/tex]

[tex]z*4=[/tex]

Step 4: Commutative Property of Multiplication

This states that:

[tex]ab=ba[/tex]

So, we have:

[tex]z*4=[/tex]

[tex]z*4 = 4*z[/tex]

[tex]z*4 = 4z[/tex]

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