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

Question

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

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

Video Solution

Step-by-Step Solution

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

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

We can treat (cg) (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 (cg) (c \cdot g) over the terms within the parentheses:

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

Hence, the simplified expression is:

acg+bcg acg + bcg .

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

No, acg+bcg acg + bcg .

Answer

No, acg+bcg acg+\text{bcg}