Simplify (a+b)(c·g): Applying the Distributive Property

It is possible to use the distributive property to simplify the expression

$(a+b)(c\cdot g)$

To solve this problem, we must determine if we can apply the distributive property to simplify the expression $(a+b)(c \cdot g)$.

The distributive property states that for any three terms, the expression $x(y+z)$ results in $xy + xz$. Here, we have the sum $(a + b)$ and the product $(c \cdot g)$.

We can treat $(c \cdot g)$ as a single term because it involves multiplication, which makes it like a single number or variable in terms of manipulating the expression algebraically. Therefore, using the distributive property, we distribute $(c \cdot g)$ over the terms within the parentheses:

• Step 1: Distribute $c \cdot g$ to $a$, yielding $acg$.
• Step 2: Distribute $c \cdot g$ to $b$, yielding $bcg$.

Hence, the simplified expression is:

$acg + bcg$.

Therefore, the correct answer, according to the choices provided, is:

No, $acg + bcg$.