Question
How many terms will there be in the expansion of the expression
. Explain how you know?
The correct answer is: The numbers of combination permutations are n+1. Hence, the expansion would have n+1 terms.
ANSWER:
Hint:
The expansion of the expression 
would have n+1 terms. The binomial expansion is 
, here 
.
We are asked to explain and find the numbers of terms in the expansion of .
Step 1 of 1:
The given expression is . The value of n=3. Consider the binomial theorem .Here, the combination permutations are:
..............,
Which form the coefficients of the expansion.
The numbers of combination permutations are n+1. Hence, the expansion would have n+1 terms.
Note:
For the expansion of the expression , we would have n+1 terms.
Related Questions to study
Find the third term of the binomial expansion 
The expansion of (x + y)n has n+1 terms while expanding. The answer can be found using the Pascal’s triangle or binomial expansion.
Find the third term of the binomial expansion
The expansion of (x + y)n has n+1 terms while expanding. The answer can be found using the Pascal’s triangle or binomial expansion.
Factor 
in the form 
. Then find the value of a,b and c.
Factor in the form . Then find the value of a,b and c.
Find the fifth term of the binomial expansion 
The expansion of has n+1 terms while expanding. The answer can be found using the Pascal’s triangle or binomial expansion.
Find the fifth term of the binomial expansion
The expansion of has n+1 terms while expanding. The answer can be found using the Pascal’s triangle or binomial expansion.
The sum of the coefficients in the expansion of the expression 
is 64. Use Pascal’s triangle to find the value of n.
Using Pascal's Triangle, where n can be any positive integer as x and y are real numbers, one can determine the binomial coefficients of the terms of the binomial formula (x + y)n. Pascal Triangle is a type of number pattern that appears as a triangular arrangement and is represented by triangles. It starts with '1' at the top and continues with '1' on the triangle's two sides. Each new number in the Pascal triangle has equal values to the sum of the two integers above and below. The probability conditions in which this triangle is utilized vary. Every row represents this table's coefficient of expansion of (x + y)n. Zero row n = 0, (x + y)0
The sum of the coefficients in the expansion of the expression is 64. Use Pascal’s triangle to find the value of n.
Using Pascal's Triangle, where n can be any positive integer as x and y are real numbers, one can determine the binomial coefficients of the terms of the binomial formula (x + y)n. Pascal Triangle is a type of number pattern that appears as a triangular arrangement and is represented by triangles. It starts with '1' at the top and continues with '1' on the triangle's two sides. Each new number in the Pascal triangle has equal values to the sum of the two integers above and below. The probability conditions in which this triangle is utilized vary. Every row represents this table's coefficient of expansion of (x + y)n. Zero row n = 0, (x + y)0
A student says that the expansion of the expression 
has seven terms. Describe and correct
the error the student may have made ?
A student says that the expansion of the expression has seven terms. Describe and correct
the error the student may have made ?
Expand the expression 
.what is the sum of the coefficients?
Expand the expression .what is the sum of the coefficients?
Use Pascal’s triangle and the binomial theorem to expand 
. Justify your work.
Use Pascal’s triangle and the binomial theorem to expand . Justify your work.
Emma factored 
Describe and correct the error Emma made in factoring the polynomial.
A polynomial is factored when expressed as the product of more than one factor; this is somewhat the opposite of multiplying. The following properties or identities, along with other methods, are typically used to factor polynomials.
¶A number is quickly factorized into smaller digits or factors of the number using the factorization formula. Finding the zeros of the polynomial expression or the values of the variables in the given expression are both made possible by factoring polynomials.
¶There are many ways to factorize a polynomial of the form axn + bxn - 1 + cxn - 2+ ........., px + q, including grouping, using identities, and substituting.
Emma factored Describe and correct the error Emma made in factoring the polynomial.
A polynomial is factored when expressed as the product of more than one factor; this is somewhat the opposite of multiplying. The following properties or identities, along with other methods, are typically used to factor polynomials.
¶A number is quickly factorized into smaller digits or factors of the number using the factorization formula. Finding the zeros of the polynomial expression or the values of the variables in the given expression are both made possible by factoring polynomials.
¶There are many ways to factorize a polynomial of the form axn + bxn - 1 + cxn - 2+ ........., px + q, including grouping, using identities, and substituting.
using binomial theorem.
where 
a coefficient of row k of Pascal’s triangle is, p is the probability of success, and q is the probability of failure.
. The Identity 
can be used to generate Pythagorean triples. Use the identity to generate a Pythagorean triple when x = 5 and y = 4
.
