$$\textbf{\textcolor{#4257b2}{Challenge}}$$

Find a simpler expression equivalent to $\dfrac{3a + 6}{2a + 4}$.

Evaluate.

$3(2a + b)$ for $b = 4$ and $a = 2$

Write as an algebraic expression.

$b$ more than $a$

Write using exponential notation.

$$10 \cdot 10 \cdot 10 \cdot 10 \cdot 10 \cdot 10$$

Calculate.

$$(7 + 2)^2$$

Solve for the given replacement set.

$$x^2 + x = 0\ \ \ \{0, 100, 1000\}$$

Solve using the Try, Test, Revise strategy.

$$7(14 - \Box) = 35$$

Use the distributive property to write an equivalent expression.

$$4(1 + y)$$

Write an equivalent expression using a commutative property.

$$ab + c$$

Evaluate.

$(3a^3)$ for $a = 5$

$\textbf{\textcolor{#4257b2}{Mathematical Reasoning}} \hspace{15pt}$ A student factored $ax + ay + bx + by$ as $a(x + y) + b(x + y)$. Another student factored the same expression as $x(a + b) + y(a + b)$. Are both answers correct, or is one of them incorrect? Justify your answer.

Factor.

$$8 + 16x + 40y$$

Factor.

$$20a + 30b$$

$\textbf{\textcolor{#4257b2}{Critical Thinking}} \hspace{15pt}$ You know that $a(b + c) = ab + ac$ for any numbers $a, b,$ and $c$. Use this fact and the properties introduced earlier to write a paragraph explaining why $(b + c)a = ba + ca$ is also true for any numbers $a, b,$ and $c$.