Use the distributive property to rewrite the expression.
$8(z-7)$
Answer (1)
Apply the distributive property: 8 ( z − 7 ) = 8 ( z ) + 8 ( − 7 ) .
Perform the multiplication: 8 ( z ) = 8 z and 8 ( − 7 ) = − 56 .
Combine the terms: 8 z − 56 .
The rewritten expression is 8 z − 56 .
Explanation
Understanding the Distributive Property We are asked to use the distributive property to rewrite the expression 8 ( z − 7 ) . The distributive property states that for any real numbers a , b , and c , we have a ( b + c ) = ab + a c . In our case, a = 8 , b = z , and c = − 7 .
Applying the Distributive Property Applying the distributive property to the given expression, we have:
8 ( z − 7 ) = 8 ( z ) + 8 ( − 7 )
Simplifying the Expression Now, we simplify the expression by performing the multiplication:
8 ( z ) + 8 ( − 7 ) = 8 z − 56
So, the rewritten expression is 8 z − 56 .
Final Answer Therefore, using the distributive property, we have rewritten the expression 8 ( z − 7 ) as 8 z − 56 .
Examples
The distributive property is useful in many real-life situations. For example, suppose you are buying 8 identical gift baskets, each containing a toy that costs z dollars and a chocolate bar that costs 7 dollars. The total cost of the gift baskets can be calculated as 8 ( z + 7 ) . Using the distributive property, you can rewrite this as 8 z + 8 × 7 = 8 z + 56 . This means you are spending 8 z dollars on the toys and 56 dollars on the chocolate bars.
