Question

How do you solve $6\left( {x + 3} \right)$ using the distributive property?

Answer 1

Hint: Here we need to simplify the given algebraic expression using the distributive property. We will first multiply the outside number with the inside numbers and then we will find the sum of these products by adding the product and the simplified value after the addition of the products gives the required value.

Complete step by step solution:
Here we need to simplify the given algebraic expression using the distributive property and the given algebraic expression is $6\left( {x + 3} \right)$.
If $a$, $b$ and $c$ are three real numbers, then according to the distributive property of multiplication.
$a \cdot \left( {b + c} \right) = a \cdot b + a \cdot c$
Now, we will have the distributive property of multiplication. We will simplify the expression step by step using this property.
For that, we will multiply the outside number i.e. 4 with the numbers inside the parenthesis.
$ 6\left( {x + 3} \right) = 6 \times x + 6 \times 3$
On multiplying the terms, we get
$ \Rightarrow 6\left( {x + 3} \right) = 6x + 18$
We can simplify the terms further as there are no terms in the expression.

Therefore, the simplified value of the given algebraic expression is equal to $6x + 18$.

Note:
Here we have obtained the simplified value of the given algebraic expression. The algebraic expression used in the question is a linear algebraic expression because the degree of the expression is 1. We have also used various mathematical operations to solve the given algebraic expression. So we need to remember that when we multiply two positive numbers together then the resultant value will also be a positive number and when we multiply two negative numbers together then the resultant value will be a positive number.