Question
Use Pascal’s triangle and the binomial theorem to expand 
. Justify your work.
The correct answer is: Thus, the expansion is; .
ANSWER:
Hint:
Pascal's Triangle is a method to know the binomial coefficients of terms of binomial expression (x + y)n, where n can be any positive integer and x,y are real numbers. Pascal Triangle is represented in a triangular form, it is kind of a number pattern in the form of a triangular arrangement.
The binomial expansion is 
, here 
.
We are asked to find expansion of the expression using Pascal’s triangle and binomial theorem.
Step 1 of 3:
The given expression is . Here n=4. Thus, we would have 4+1=5 terms in the expansion.
Here,
.
Step 2 of 3:
Find the fifth row of the Pascal’s triangle to get the coefficients of .
Thus, the expansion is:
Hence, the expansion is;
Step 3 of 3:
Substitute the values of in the binomial expansion to get the terms.
Thus, we haThus, the expansion is; .
The answer obtained using binomial theorem and Pascal’s triangle are the same. We can use both methods to find the answer.
Note:
We can use both the binomial theorem and the Pascal’s triangle to get the expansion of any expressions.
Related Questions to study
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
.
.
cubic units.
.
