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

Answer 1

First, let's apply the distributive property to each term inside the parentheses:

2(a + 5) = 2a + 10
4(2a + 3) = 8a + 12

Now, let's rewrite the original expression with the simplified terms:

2(a + 5) + 4(2a + 3) - 10 = (2a + 10) + (8a + 12) - 10

Now, let's apply the associative property by grouping like terms together:

(2a + 8a) + (10 + 12) - 10 = 10a + 22 - 10

Simplify further:

10a + 22 - 10 = 10a + 12

Therefore, an expression equivalent to 2 (a+5) + 4 (2a+3) - 10 using the Associative and Commutative properties is 10a + 12.