Question

How do you use distributive property to simplify \[7(z - 4)\]?

Answer 1

Hint: We use the distributive property of multiplication over subtraction in this question. We multiply the number or value given outside the bracket to each of the values inside the bracket with the subtraction sign in between them. Apply BODMAS rule and solve the equation step-wise.
* Distributive Property: For any three numbers ‘a’, ‘b’ and ‘c’ we can write \[a(b - c) = ab - bc\]
* BODMAS rule: If we are given any equation, then we solve any equation in stepwise manner of bracket, order, Division, multiplication, addition and then subtraction.

Complete step-by-step answer:
Here we have to simplify \[7(z - 4)\]
We use the distributive property of multiplication over subtraction here to open the value.
We know the distributive property of multiplication over subtraction is given by the formula \[a(b - c) = ab - bc\]
\[ \Rightarrow 7(z - 4) = \left( {7 \times z} \right) - \left( {7 \times 4} \right)\]
Now calculate each of the products in the brackets on right hand side of the equation
\[ \Rightarrow 7(z - 4) = 7z - 28\]

\[\therefore \]The simplified value of \[7(z - 4)\] is \[7z - 28\].

Note:
Many students make the mistake of not writing the products after opening the value using distributive property in brackets and students get confused as they write the answer as \[\left( {7z - 4} \right)\] which is wrong. Keep in mind we have to keep both obtained products from distributive property in brackets and then open after we have multiplied the values inside the bracket. This mistake is done by the students when they don’t know the BODMAS rule or they forget to apply it in a hurry. We should remember that we solve any equation in stepwise manner of bracket, order, Division, multiplication, addition and then subtraction that is the BODMAS rule.