Let's work through some of the problems from your image. I'll start by solving the first few questions and provide detailed explanations.

Problem 7: Simplify the expression

$a(b + c - bc) - b(c + a - ac) + c(b - a)$ We distribute the terms: $a(b + c - bc) = ab + ac - abc$ $- b(c + a - ac) = -bc - ab + abc$ $c(b - a) = cb - ca = bc - ac$ Now, let's combine all the terms: $ab + ac - abc - bc - ab + abc + bc - ac$ Notice that several terms cancel out: $ab - ab + ac - ac - abc + abc - bc + bc = 0$ Thus, the simplified expression is 0.

Answer: E).

Problem 8: If $a + b + 3 = 10$, find the value of:

$3a + 7, 7 + 1, 7b + 2, 5a + 11, 2 + 4, 6b$ First, solve $a + b = 7$ from $a + b + 3 = 10$.

Now, calculate the expressions one by one: $3a + 7$ $7 + 1 = 8$ $7b + 2$ $5a + 11$ [ 2 +