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)

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Verified Answer :

dsaketh dsaketh · Answer 1 · 2017-02-26T13:05:32-05:00

The last ones is equivalent and the rest are not

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ColinJacobus ColinJacobus · Answer 2 · 2019-08-17T14:35:04-04:00

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

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

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

\((12w+20z)+(4w+10z)+2z\\\\=12w+20z+4w+10z+2z\\\\=16w+32z eq18w+30z.\)

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.