
What is the formula of ?
Answer
434.1k+ views
Hint: We can derive the formula with or without using a standard formula that is available. Even though we have a standard formula for we can derive them by splitting them into its factors. Then multiplying those factors will give us the formula for . We can also use any other standards formula to expand the factors.
Formula: The formula that we will be using for this is:
Complete step by step answer:
It is given that we aim to find the formula for this term. First, we will split the term into its factors.
Let us split into its factors. Using the formula let’s split the given term by taking as .
Now we can use the formula to split the term or we can just split that like by taking as .
Let us solve the problem in both ways.
First, let us use the formula to split the term .
Now let us multiply the factors & term by term.
Now let us group the like terms.
On simplifying this we get
Now let’s rearrange the above expression.
Let’s take the term commonly out of the last two terms.
Therefore, we get .
Note: We can see that the formula can be derived by two methods: with standard formula or without standard formula. We will get the same answer for both methods.
Now let’s derive the formula without using the standard formula.
Consider the given term .
Let’s split them into its factors using the formula .
Now let’s multiply the first two factors.
On simplifying this we get
Now let’s multiply the third term to the resultant.
Let us group the terms like.
On simplifying this we get
Let us re-arrange the above expression.
Let’s take the term commonly out of the last two terms.
Thus, we got the same answer for both methods. Therefore, the formula for the given term is .
Formula: The formula that we will be using for this is:
Complete step by step answer:
It is given that
Let us split
Now we can use the formula
Let us solve the problem in both ways.
First, let us use the formula
Now let us multiply the factors
Now let us group the like terms.
On simplifying this we get
Now let’s rearrange the above expression.
Let’s take the term
Therefore, we get
Note: We can see that the formula can be derived by two methods: with standard formula or without standard formula. We will get the same answer for both methods.
Now let’s derive the formula without using the standard formula.
Consider the given term
Let’s split them into its factors using the formula
Now let’s multiply the first two factors.
On simplifying this we get
Now let’s multiply the third term to the resultant.
Let us group the terms like.
On simplifying this we get
Let us re-arrange the above expression.
Let’s take the term
Thus, we got the same answer for both methods. Therefore, the formula for the given term
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