Question

How do you simplify \[ - 6(x + 4)?\]

Answer 1

Hint: We can solve the question by using the Distributive Property. Distributive property tells us that if a mathematical expression is in the form of \[(a + b) \cdot c\], then multiplying each of the addends from the equation separately gives us the same answer as multiplying the sum of the numbers (within the bracket) by another number (outside the bracket)

Formula used: \[(a + b) \cdot c = ac + bc\]

Complete step-by-step solution:
The given mathematical expression is:
\[ - 6(x + 4)\]
Distributive property says that multiplying each of the addends from the equation separately gives us the same answer as multiplying the sum of the numbers (within the bracket) by another number (outside the bracket). The formula for distributive property is:
\[(a + b) \cdot c = ac + bc\]
When we apply this property in our mathematical expression, then we get:
\[ = ( - 6 \cdot x) + ( - 6 \cdot ( + 4))\]
Here, the brackets are opened and \[ - 6\]is multiplied to both the numbers that were in the bracket.
Now, we will multiply both the term and get:
\[ = - 6x + ( - 24)\]
\[ = - 6x - 24\]
\[ \Rightarrow - 6(x + 4) = - 6x - 24\]
This is our final answer. The simplified version of \[ - 6(x + 4)\]is \[ - 6x - 24\].

Additional information: This distributive property is also called the distributive law of division and multiplication. We should make sure that when we multiply the outside number with all the terms that are in the bracket, they should not get mixed up. This usually happens when there are many terms in the expression.

Note: We usually first add the numbers inside the bracket and then multiply it with the outside term. But we should not do that. We should multiply each term that is inside the bracket with the outside number and then add all the terms. This is usually done when the two numbers inside the bracket cannot be added because they are not like terms.