Question

which expression is equivalent to 5(6t + 2) + 5t?
35t + 2
11t + 10
(6t + 2)5 + 5t
10t + 35

Explanation:

Step1: Expand the expression

Use the distributive property \(a(b + c)=ab+ac\). Here \(a = 5\), \(b = 6t\), \(c = 2\). So \(5(6t + 2)=5\times6t+5\times2=30t + 10\).

Step2: Combine like - terms

The original expression \(5(6t + 2)+5t\) becomes \(30t + 10+5t\). Combine the \(t\) - terms \(30t\) and \(5t\): \(30t+5t = 35t\). So the simplified expression is \(35t + 10\). Among the given options, the equivalent expression is \((6t + 2)5+5t\) (since multiplication is commutative, \(5(6t + 2)=(6t + 2)5\)).

Answer:

C. \((6t + 2)5+5t\)