Question

How do you find the product (x+3)(x+3) ?

Answer 1

Hint: This question is from the topic of algebra. In this question, we will find the product of the term $\left(x+3 \right) \left(x+3 \right)$. In solving this question, we will use the foil method. Before using the foil method, we will first understand the foil method. After that, we will solve and find the product. After that, we will see the alternate method to solve this question.

Complete step by step solution:
Let us solve this question.
This question has asked us to find the product of a given term. The given term is $\left(x+3 \right) \left(x+3 \right)$.
Before finding the product of the term $\left(x+3 \right) \left(x+3 \right)$, let us first understand the foil method.
According to foil method, we can write the term $\left(a+b \right) \left(c+d \right)$ as
\[\left( a+b \right)\left( c+d \right)=a\left( c+d \right)+b\left( c+d \right)\]
The above equation can also be written as
\[\Rightarrow \left( a+b \right)\left( c+d \right)=a\times c+a\times d+b\times c+b\times d=ac+ad+bc+bd\]
So, foil method says that $\left(a+b \right) \left(c+d \right)$ can also be written as $ac+ad+bc+bd$
Or, we can write
$(a+b)(c+d)= ac+ad+bc+bd$
So, using foil method, we can write the term $\left(x+3\right)\left(x+3\right)$ as
\[\left( x+3 \right)\left( x+3 \right)=x\times x+x\times 3+3\times x+3\times 3\]
The above equation can also be written as
\[\Rightarrow \left( x+3 \right)\left( x+3 \right)={{x}^{2}}+3x+3x+{{3}^{2}}\]
The above equation can also be written as
\[\Rightarrow \left( x+3 \right)\left( x+3 \right)={{x}^{2}}+6x+{{3}^{2}}\]
As we know that the square of 3 is 9, so we can write the above equation as
\[\Rightarrow \left( x+3 \right)\left( x+3 \right)={{x}^{2}}+6x+9\]
Now, we have found the product of \[\left( x+3 \right)\left( x+3 \right)\]. The product is \[{{x}^{2}}+6x+9\].

Note: As we can see that this question is from the topic of algebra, so we should have a better knowledge in that topic. We should know about the foil method to solve this type of question easily.
The foil method says that $\left(a+b \right) \left(c+d \right)$ can also be written as $ac+ad+bc+bd.$
We can solve this question by an alternate method.
For that, we should know the following formula:
\[{{\left( a+b \right)}^{2}}={{a}^{2}}+2\times a\times b+{{b}^{2}}\]
Now, as we know that x multiplied two times can be written as the square of x. So, we can write
\[\left( x+3 \right)\left( x+3 \right)={{\left( x+3 \right)}^{2}}\]
Now, using the formula \[{{\left( a+b \right)}^{2}}={{a}^{2}}+2\times a\times b+{{b}^{2}}\], we can write
\[\Rightarrow \left( x+3 \right)\left( x+3 \right)={{x}^{2}}+2\times x\times 3+{{3}^{2}}\]
The above equation can also be written as
\[\Rightarrow \left( x+3 \right)\left( x+3 \right)={{x}^{2}}+6x+9\]
Hence, we have the same answer from this method. So, we can use this method too to solve this type of question.