Question

write an expression that is equivalent to 5(a + 3b) + 6 + 8a + 12. 5(a + 3b) + 6 + 8a + 12 = \square a + ? b + ?

Explanation:

Step1: Distribute the 5

Using the distributive property \( c(a + b)=ca+cb \), we distribute 5 to \( a \) and \( 3b \):
\( 5(a + 3b)=5a + 15b \)

Step2: Combine like terms for \( a \)

Now, combine the \( a \)-terms: \( 5a + 8a \).
\( 5a + 8a = 13a \)

Step3: Combine constant terms

Combine the constant terms (6 and 12):
\( 6 + 12 = 18 \)

Step4: Write the simplified expression

The \( b \)-term remains \( 15b \) (no other \( b \)-terms to combine). So the simplified expression is \( 13a + 15b + 18 \).

Answer:

For the coefficient of \( a \): \( 13 \), for \( b \): \( 15 \), and the constant term: \( 18 \). So the blanks are filled as \( 13 \), \( 15 \), and \( 18 \) respectively.