Expand and simplify $5(2 a+3)+4$
Answer (1)
Distribute the 5: 5 ( 2 a + 3 ) = 10 a + 15
Substitute back into the original expression: ( 10 a + 15 ) + 4
Combine the constant terms: 10 a + 15 + 4 = 10 a + 19
The simplified expression is: 10 a + 19
Explanation
Understanding the Problem We are given the expression 5 ( 2 a + 3 ) + 4 and our goal is to expand and simplify it. This means we need to get rid of the parentheses by distributing the 5 and then combine any like terms to make the expression as simple as possible.
Distributing the 5 First, we distribute the 5 to both terms inside the parentheses: 5 ( 2 a + 3 ) = 5 ( 2 a ) + 5 ( 3 ) = 10 a + 15
Substituting Back Now, we substitute this back into the original expression: 5 ( 2 a + 3 ) + 4 = ( 10 a + 15 ) + 4
Combining Like Terms Finally, we combine the constant terms 15 and 4: 10 a + 15 + 4 = 10 a + 19
Final Answer So, the expanded and simplified expression is 10 a + 19 .
Examples
Let's say you're buying multiple items at a store. You want to buy 5 of the same item, which costs '2a+3' dollars each, where 'a' is some variable (maybe representing a discount or extra charge). Then you have an additional fixed cost of $4 (maybe a shipping fee). The expression 5 ( 2 a + 3 ) + 4 helps you calculate the total cost. Simplifying it to 10 a + 19 makes it easier to quickly compute the total cost for different values of 'a'. For example, if 'a' is 1, the total cost is $10(1)+19 = $29.
