Question

Directions: Drag each expression to the correct location on the table. Identify each expression as either equivalent to or not equivalent to 18w + 30z.
2(9w + 6z) + 9(2z)

2(9z + 9w) + 12w

(12w + 20z) + (4w + 10z) + 2z

6(5z + 3w)

Answer 1

The last ones is equivalent and the rest are not

Answer 2

Answer: Expressions (A), (D) are equivalent and (B), (C) are NOT equivalent to the given expression.

Step-by-step explanation:  We are given to identify each expression as either equivalent or not equivalent to the following expression :

$E=18w+30z.$

(A) The given expression is $2(9w+6z)+9(2z).$

The simplified form of the above expression is

$2(9w+6z)+9(2z)\\\\=18w+12z+18z\\\\=18w+30z.$

So, expression (A) is equivalent to the given expression.

(B) The given expression is $2(9z+9w)+12z.$

The simplified form of the above expression is

$2(9z+9w)+12z\\\\=18z+18w+12z\\\\=18z+30w\neq 18w+30z.$

So, expression (B) is NOT equivalent to the given expression.

(C) The given expression is $(12w+20z)+(4w+10z)+2z.$

The simplified form of the above expression is

$(12w+20z)+(4w+10z)+2z\\\\=12w+20z+4w+10z+2z\\\\=16w+32z\neq18w+30z.$

So, expression (C) is NOT equivalent to the given expression.

(D) The given expression is $6(5z+3w).$

The simplified form of the above expression is

$6(5z+3w)=30z+18w=18w+30z.$

So, expression (D) is equivalent to the given expression.

Thus, (A), (D) are equivalent and (B), (C) are NOT equivalent to the given expression.