Answer

Verified

453.6k+ views

**Hint:**Using the formula of \[{{\text{(a + b)}}^{\text{2}}}{\text{ = }}{{\text{a}}^{\text{2}}}{\text{ + }}{{\text{b}}^{\text{2}}}{\text{ + 2ab}}\] in the above question and also applying the binomial expansion in the above question we will get the required form of the equation. Also use the concept that for \[{{\text{(a + b)}}^{\text{n}}}\]total number of terms are \[{\text{n + 1}}\].

**Complete step by step answer:**

As per the given equation is \[{{\text{(1 + 2x + }}{{\text{x}}^{\text{2}}}{\text{)}}^{{\text{10}}}}\]

As first observing the above given equation and converting it into the simpler form as

\[{\text{1 + 2x + }}{{\text{x}}^{\text{2}}}\]= \[{{\text{x}}^{\text{2}}}{\text{ + }}{{\text{1}}^{\text{2}}}{\text{ + 2(1)(x)}}\]=\[{{\text{(x + 1)}}^2}\]

And hence replacing it in the above equation, we get,

\[{{\text{(1 + 2x + }}{{\text{x}}^{\text{2}}}{\text{)}}^{{\text{10}}}} = {{\text{(x + 1)}}^{20}}\]

And hence using the above concept of for \[{{\text{(a + b)}}^{\text{n}}}\]total number of terms are \[{\text{n + 1}}\].

So, the total number of terms will be \[21\]

Hence, option (c) is our correct answer.

**Note:**The Binomial theorem states us the way and definite procedure of expanding expressions of the form \[{{\text{(a + b)}}^{\text{n}}}\]. A binomial has two terms. By definition, a binomial is a polynomial with exactly two terms. The bottom number of the binomial coefficient is \[{\text{r - 1}}\], where r is the term number. a is the first term of the binomial and its exponent is n – (\[{\text{r - 1}}\]), where n is the exponent on the binomial and r is the term number. b is the second term of the binomial and its exponent is \[{\text{r - 1}}\], where r is the term number.

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

Harsha Charita was written by A Kalidasa B Vishakhadatta class 7 social science CBSE

Which are the Top 10 Largest Countries of the World?

Banabhatta wrote Harshavardhanas biography What is class 6 social science CBSE

Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE