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`

`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`

` `

"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**