Simplify: 3d x d

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durbanville's profile pic

durbanville | High School Teacher | (Level 2) Educator Emeritus

Posted on

When simplifying expressions consider the operation (ie `+ - times divide` ) and, use the rules of algebra to simplify correctly. 

In this expression, `d` is known as a "variable." This is because we do not know it's value and therefore it may "vary" according to the expression in which it appears. Letters, and most commonly `x` , are used as variables to signify unknown quantities in algebra and work well in problem solving. 

In this expression, the 3 is known as a "constant," because it will always represent a 3 and so it is certainly constant. 

We are multiplying the unknown variable, d by 3 a constant and then by another of the same variable, d. The 3, therefore, will not be affected by the multiplication of `3d times d= 3d^2`

The result would have been different if we were adding the ds because 3d + 1d is when the constant 3 is added to the constant 1 to make 4d. Imagine adding 3 apples and 1 apple. You get 4 apples, not 4 apples to the power of 2. 

Ans:

`3d times d = 3d^2`

mrskk's profile pic

mrskk | (Level 1) Adjunct Educator

Posted on

3d x d 

Since d is the common term, the 3 will stay the same and you will multiply dxd to get d^2.

Your final answer will be 3d^2

aishukul's profile pic

aishukul | Student, Grade 10 | (Level 3) Honors

Posted on

`3d*d=`

`3d^2`

When multiplying exponents, you add the powers of the exponents. Since d by itself has the power of 1, multiplying two d's gives you `d^2:`

`d^1*d^1=d^2`

`d^(1+1)=d^2`

``Also, 3 times 1 (since it is assumed that a variable with no coefficient in front of it has a coefficient of 1) is 3. So, 3d times d =

`3d^2`

` `

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sam-lippai | eNotes Newbie

Posted on

"3d x d"

When d is multiplied by itself it squares, just like any number (e.g: 3 x 3 = 3^2).

Thus in this circumstance d x d = d^2

When d is multiplied by 3, it is equal to 3d. When the variable (d) is next to the number it is multiplied by, they form together. Basically 3d is 3 x d but just simplified.

Therefore, 3d x d = 3d^2 

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