Question

How do you use the distributive property to simplify $7\left( {z - 4} \right)$?

Answer 1

Hint: In distributive property of multiplication over subtraction, we can subtract the numbers and then multiply, or we can multiply and then subtract. So, first $7$ is multiplied with $4$, then the product is subtracted from the product of $7$ and $z$. Then, we will get the simplified version of $7\left( {z - 4} \right)$.

Formula used: Distributive property of multiplication over subtraction:
Let $a$, $b$ and $c$ be three real numbers, then
 $a \times (b - c) = (a \times b) - (a \times c)$

Complete step-by-step solution:
To “distributive” means to divide something or give a share or part of something.
According to the distributive property, multiplying the difference of two numbers will give the same result as multiplying each addend individually by the number and then subtracting the products.
The distributive property helps in making difficult problems simpler by writing it in simpler form.
The distributive property of multiplication is used to rewrite expression by distributing or breaking down a factor as a sum or difference of two numbers.
We can subtract the numbers and then multiply, or we can multiply and then subtract.
Here, $7\left( {z - 4} \right)$
So, first $7$ is multiplied with $4$, then the product is subtracted from the product of $7$ and $z$.
$7\left( {z - 4} \right) = \left( {7 \times z} \right) - \left( {7 \times 4} \right)$
So, Multiplying $7$ with $z$, and multiplying $7$ with $4$, we get
$7\left( {z - 4} \right) = 7z - 24$

Therefore, the simplified version of $7\left( {z - 4} \right)$ is $7z - 24$.

Note: The distributive property of addition and subtraction can be used to rewrite expressions for a variety of purposes. When we are multiplying a number by a sum, we can add and then multiply. We can also multiply each addend first and then add the products.
Even though division is the inverse of multiplication, the distributive law only holds true in case of division, when the dividend is distributed or broken down. For instance, using the distributive law for $132 \times 6$, $132$ can be broken down as $60 + 60 + 12$, thus making division easier. However, $132 \times \left( {4 + 2} \right)$ will give you the wrong result.