Question

Apply the associative and commutative properties to generate an expression equivalent to 2 (a+5) + 4 (2a+3 - 10

Answer 1

To apply the associative property, we group terms that involve the same variable together. We can also combine like terms to simplify the expression.

Let's start with 2(a + 5) + 4(2a + 3 - 10):

First, simplify the expression within the parentheses:

2(a + 5) + 4(2a - 7)

Now, distribute the coefficients to each term inside the parentheses:

2a + 10 + 8a - 28

Next, combine like terms:

(2a + 8a) + (10 - 28)

10a - 18

So, the expression equivalent to 2(a + 5) + 4(2a + 3 - 10) is 10a - 18.