Let's analyze the expressions for each student to determine which statement is NOT true.

1. Josie:

Expression: $-4(2x - 4)$

Simplify: $-4(2x - 4) = -4 \cdot 2x + (-4) \cdot (-4) = -8x + 16$ Josie's simplified expression is $-8x + 16$, which matches statement a.

2. Igor:

Expression: $2 + 3(10 - 5x)$

Simplify: $3(10 - 5x) = 3 \cdot 10 + 3 \cdot (-5x) = 30 - 15x$ Thus: $2 + 30 - 15x = 32 - 15x$ Igor's simplified expression is $32 - 15x$, but statement b claims it simplifies to $2 + 15x$, which is incorrect.

3. Rachel:

Expression: $\frac{1}{3}(-12x + 9)$

Simplify: $\frac{1}{3} \cdot (-12x) + \frac{1}{3} \cdot 9 = -4x + 3$ Rachel's simplified expression is $-4x + 3$, which matches statement c.

4. Milo:

Expression: $7(6 - x) + 13x$

Simplify: $7(6 - x) = 7 \cdot 6 - 7 \cdot x = 42 - 7x$ Thus: $42 - 7x + 13x = 42 + 6x$ Milo's simplified expression is $6x + 42$, which matches statement d.

Conclusion:

The incorrect statement is b (Igor's expression does not simplify to $2 + 15x$).

Would you like more details or further clarification on this?

Here are 5 related questions for further exploration:

1. How do you distribute terms in parentheses when simplifying an algebraic expression?
2. What are common mistakes to avoid when simplifying expressions?
3. How do coefficients affect terms during distribution?
4. How can you check your simplification for accuracy?
5. What are the steps to simplify complex fractions in algebra?

Tip: Always distribute the number outside the parentheses to all terms inside the parentheses to avoid mistakes in simplification.