Which property was used to simplify the expression? \[ 4(b+2)=4 b+8 \] distributive property commutative property associative property inverse property

Ah, the distributive property swoops in like a superhero here! It allows you to distribute that 4 across everything in the parentheses. So, 4 times b is 4b, and 4 times 2 is 8, giving you \( 4(b+2) = 4b + 8 \). Easy-peasy! Now, let's not forget that the other properties have their star moments too! The commutative property changes the order of numbers in addition or multiplication (like switching dance partners), while the associative property groups numbers without changing the result. However, in this case, it was the distributive property that saved the day!