Question

simplifying variable expressions with distribution
simplify this expression.
3 + 3(4 + 4h) + 3h

Explanation:

Step1: Expand the expression

Use the distributive property \(a(b + c)=ab+ac\). Here \(a = 3\), \(b = 4\), \(c = 4h\).
\(3+3(4 + 4h)+3h=3+(3\times4+3\times4h)+3h=3+(12 + 12h)+3h\)

Step2: Remove the parentheses

\(3+(12 + 12h)+3h=3 + 12+12h+3h\)

Step3: Combine like - terms

Combine the constant terms \(3+12\) and the variable terms \(12h+3h\).
For the constant terms: \(3+12 = 15\)
For the variable terms: \(12h+3h=(12 + 3)h=15h\)

Answer:

\(15h + 15\)