Question

How do you express $\left( {3x + 3} \right)\left( {2x + 6} \right)$ as a trinomial??

Answer 1

Hint: The definition of trinomial is a math equation that has three terms that are connected by plus or minus notation. In this question, we will multiply each term in the left parentheses by an individual term in the right parentheses. This is known as distributive low. And then, after simplifying the algebraic expression we will get the final answer.

Complete step-by-step answer:
In this question, we want to find a trinomial of the equation
$ \Rightarrow \left( {3x + 3} \right)\left( {2x + 6} \right)$
If we want to multiply a sum by another number, we can multiply each term of the sum by the number. Therefore, to multiply these two terms, we will multiply each term in the left parentheses by the individual term in the right parentheses.
$ \Rightarrow 3x\left( {2x + 6} \right) + 3\left( {2x + 6} \right)$
Now, let us apply distributive low.
 $ \Rightarrow \left( {3x \times 2x} \right) + \left( {3x \times 6} \right) + \left( {3 \times 2x} \right) + \left( {3 \times 6} \right)$
By applying this low to algebraic expressions containing parentheses we can obtain equivalent expressions without parentheses.
$ \Rightarrow 6{x^2} + 18x + 6x + 18$
Let us add 18x and 6x. So, we will get the answer is equal to
$ \Rightarrow 6{x^2} + 24x + 18$

Hence, we got the algebraic expression of the trinomial form.

Note:
There is an alternative method to solve this question. In this method, we will use the FOIL method. FOIL stands for First, Outer, Inner, and Last. We will add the results of each piece with its sign. Here, the subtraction sign should be seen as a negative.
Let us apply this method in our question.
$ \Rightarrow \left( {3x + 3} \right)\left( {2x + 6} \right)$
First: 3x times 2x.
Outer: 3x times 6.
Inner: 3 times 2x.
Last: 3 times 6
Now, add all these together.
We will get,
$ \Rightarrow 6{x^2} + 18x + 6x + 18$
Let us add 18x and 6x. So, we will get
$ \Rightarrow 6{x^2} + 24x + 18$
Hence, we got the algebraic expression of the trinomial form.