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

Answer 1

Using the Associative Property, we can rearrange the terms within the parentheses:

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

Now, combining like terms gives:

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

Finally, applying the Commutative Property allows us to rearrange the terms:

10a + 22 - 10
= 10a - 10 + 22
= 10(a - 1) + 22

Therefore, the expression equivalent to 2(a + 5) + 4(2a + 3) - 10 using the Associative and Commutative Properties is 10(a - 1) + 22.