###### Exercise43

A student has (correctly) simplified an algebraic expression in the following steps. Between each pair of steps, identify the algebraic property that justifies moving from one step to the next.

\(\phantom{={}}{7\!\left(y+4\right)+3y}\)

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

distributive property

\(={\left(7y+28\right)+3y}\)

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

distributive property

\(={\left(28+7y\right)+3y}\)

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

distributive property

\(={28+\left(7y+3y\right)}\)

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

distributive property

\(={28+\left(7+3\right)y}\)

\(={28+10y}\)

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

distributive property

\(={10y+28}\)