Question

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

To apply the Associative Property on 2 (a + 5) and 4 (2a + 3), we will group the terms with a, the constant terms, and the coefficients separately.

First, let's group the terms with a:
2(a + 5) + 4(2a + 3) - 10
= 2a + 10 + 8a + 12 - 10
= (2a + 8a) + (10 + 12 - 10)
= 10a + 12

Next, let's group the constant terms:
2(a + 5) + 4(2a + 3) - 10
= 2a + 10 + 8a + 12 - 10
= (10 + 12 - 10) + (2a + 8a)
= 12 + 10a

Finally, let's group the coefficients:
2(a + 5) + 4(2a + 3) - 10
= 2a + 10 + 8a + 12 - 10
= (2a + 8a) + (10 - 10) + (10 + 12)
= 10a + 22

Therefore, the expression equivalent to 2(a + 5) + 4(2a + 3) - 10 using the Associative Property is 10a + 12 or 12 + 10a or 10a + 22.