Question

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

Explanation:

Step1: Expand the expression

Use the distributive property \(a(b + c)=ab+ac\) on \(3(4 + 4h)\).
\(3(4 + 4h)=3\times4+3\times4h = 12+12h\).
The original expression \(3 + 3(4 + 4h)+3h\) becomes \(3+12 + 12h+3h\).

Step2: Combine like terms

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

Answer:

\(15+15h\)