Use the distributive property to write an equivalent expression. A.) (3•y)•z B.) x + (y + 21)

Answer 1

A)

The expression is (3•y)•z

Using associative property of multiplication: (a•b)•c=a•(b•c) , we get,

(3•y)•z  = 3•(y•z)

Equivalent expression is 3•(y•z)

 

B)

The expression is x +(y + 21)

Using associative property of addition: (a+b)+c=a+(b+c) , we get,

x +(y + 21) = (x + y) +21

Equivalent expression is (x + y) +21

Answer 2

A) The expression is (3*y)*z

(a*b)*c = a*(b*c) is associative property for multiplication.

(3*y)*z = 3*(y*z)

3y *z = 3*yz

3yz = 3yz

(3*y)*z

a = 3, b = y and c = z.

(3*y)*z

= (3y)*z

= 3yz

Equivalent expression of (3*y)*z is 3yz.

B) x + (y + 21)

The distributive property a(b+c) = ab + ac

x + (y + 21) = (x + y) + 21

x + y + 21 = x + y + 21

x + (y + 21)

a = 1, b = y and c = 21

x + (y + 21) = x + y  + 21

Equivalent expression of x + (y + 21) is x + y + 21.