Question

How do you find the product of $\dfrac{1}{2}d(2d + 6)?$

Answer 1

Hint: To find the product, first of all distinguish the multiplicands present in the expression then use distributive property of multiplication over addition to multiply the multiplicands and simplify the expression. Take care of the fact that when the same variables are being multiplied then they are compressed to a single factor which is raised to the power of the number of the variables.

Complete step by step answer:
In order to find the product of $\dfrac{1}{2}d(2d + 6),$ we will find the multiplicands or factors present in the expression to be multiplied.
We can see that in the expression $\dfrac{1}{2}d(2d + 6),\;\dfrac{1}{2}d\;{\text{and}}\;(2d + 6)$ are multiplicands,
Since in the second multiplicand, that is $(2d + 6)$ it is a mixture of two terms (a variable and a constant), so to multiply with this type of multiplicands, we will use distributive property of multiplication over addition to simplify and multiply the given multiplication.
So using this property in our question, we will get
$
   = \dfrac{1}{2}d(2d + 6) \\
   = \dfrac{1}{2}d \times 2d + \dfrac{1}{2}d \times 6 \\
   = d \times d + d \times 3 \\
   = d \times d + 3d \\
 $
Now, the multiplication of the two identical variables will give the variable raise to the power two as follows
$ = {d^2} + 3d$
So ${d^2} + 3d$ is the required product of the given multiplication.

Note: When a variable and a constant is being multiplied then take care of the fact that the variable should be written after the constant or one may say the constant must be the prefix. Also you can simplify the product furthermore as you can see the variable is present in both of the terms, so take it common to simplify the product.