Question

How do you use the distributive property to write the expression without parentheses: $6\left( {a - 2} \right)$?

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. Then we will find the sum of these products by adding the product and the simplified value after the addition of the products give the required value.
Formula used:
Distributive property of multiplication over subtraction:
Let $a$, $b$ and $c$ be three real numbers, then
 $a \times (b - c) = (a \times b) - (a \times c)$

Complete step-by-step solution:
Here we need to simplify the given algebraic expression using the distributive property and the given algebraic expression is $6\left( {a - 2} \right)$.
If $a$, $b$ and $c$ are three real numbers, then according to the distributive property of multiplication.
$a \times (b - c) = (a \times b) - (a \times c)$
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. $6$ with the numbers inside the parenthesis.
$6\left( {a - 2} \right) = \left( {6 \times a} \right) - \left( {6 \times 2} \right)$
On multiplying the terms, we get
$ \Rightarrow 6\left( {a - 2} \right) = 6a - 12$
We can simplify the terms further as there are no like terms in the expression.
Therefore, the simplified value of the given algebraic expression is equal to $6a - 12$.

Note: The algebraic expression used in the question is a linear algebraic expression because the degree of the expression is 1. We need to remember that when we multiply two positive numbers together then the resultant value will also be a positive number. When we multiply two negative numbers together then the resultant value will be a positive number. There are many types of algebraic equations such as quadratic equations, cubic equations, etc. A quadratic equation is an equation that has the highest degree of 2 and also has two solutions. Similarly, a cubic equation is an equation that has the highest degree of 3 and has 3 solutions. So, we can say that the number of solutions of an equation depends on the highest degree of the equation.