Exercise44

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 multiplication

associative property of multiplication

distributive property

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

?

commutative property of multiplication

associative property of multiplication

distributive property

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

?

commutative property of multiplication

associative property of multiplication

distributive property

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

?

commutative property of multiplication

associative property of multiplication

distributive property

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

$$={28+10y}$$

?

$$={10y+28}$$