
What is the formula of ?
Answer
436.8k+ views
Hint: The question is related to the algebraic expression. In the algebra we have some standard algebraic identities for squares and cubes. So here we have to find the formula for , first we determine and then we determine .
Complete step-by-step answer:
The algebraic expression is a combination of the constants, variables and it includes the arithmetic operation symbols. In algebraic expression we have three different kinds namely, monomial, binomial and polynomial expressions.
Now we will consider the algebraic expression
Now multiply the above term by , the we have
On multiplying we have
When the same variable multiplied twice we write in the form of the exponent so we have
Therefore we have
----- (1)
Now to the equation (1) again we multiply by , we have
On multiplying we have
When the same variable multiplied twice or more we write in the form of the exponent so we have
On simplifying we have
Therefore we have
----- (2)
Take to LHS we get
This can be written as
Take as common in the RHS we have
---------- (3)
Substitute the (1) in (3) we have
On simplifying we have
Hence we have determined the value of
Therefore the formula of is
So, the correct answer is “ ”.
Note: Since the question contains the algebraic expression and formula of the algebraic identities, it is easy to solve the problem if we knew the standard algebraic formulas. We should take care of signs because they may sometimes while solving. The like terms can be cancelled or added but not unlike terms.
Complete step-by-step answer:
The algebraic expression is a combination of the constants, variables and it includes the arithmetic operation symbols. In algebraic expression we have three different kinds namely, monomial, binomial and polynomial expressions.
Now we will consider the algebraic expression
Now multiply the above term by
On multiplying we have
When the same variable multiplied twice we write in the form of the exponent so we have
Therefore we have
Now to the equation (1) again we multiply by
On multiplying we have
When the same variable multiplied twice or more we write in the form of the exponent so we have
On simplifying we have
Therefore we have
Take
This can be written as
Take
Substitute the (1) in (3) we have
On simplifying we have
Hence we have determined the value of
Therefore the formula of
So, the correct answer is “
Note: Since the question contains the algebraic expression and formula of the algebraic identities, it is easy to solve the problem if we knew the standard algebraic formulas. We should take care of signs because they may sometimes while solving. The like terms can be cancelled or added but not unlike terms.
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