Question
Use Pascal’s triangle and the binomial theorem to expand (x + 1)4 . Justify your work.
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 
.
We are asked to find expansion of the expression using Pascal’s triangle and binomial theorem
The correct answer is: Pascal’s triangle
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 have:
Thus, 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.
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 have:Thus, 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.
We can use both the binomial theorem and the Pascal’s triangle to get the expansion of any expression.
Related Questions to study
Emma factored 
Describe and correct the error Emma made in factoring the polynomial.
It is important to recall the law of exponents while to expand polynomial expressions.
Emma factored Describe and correct the error Emma made in factoring the polynomial.
It is important to recall the law of exponents while to expand polynomial expressions.
Expand 
using binomial theorem.
The answer can be found using the Pascal’s triangle. For 
, we would consider the (n+1)th row as the coefficients.
Expand using binomial theorem.
The answer can be found using the Pascal’s triangle. For , we would consider the (n+1)th row as the coefficients.
Expand using Pascal’s triangle.
The answer can be found using the binomial theorem 
Expand using Pascal’s triangle.
The answer can be found using the binomial theorem
Use binomial theorem to expand expression (x + y)7 .
The answer can be found using the Pascal’s triangle. For an expression (x + y)n , we would have n + 1 term.
Use binomial theorem to expand expression (x + y)7 .
The answer can be found using the Pascal’s triangle. For an expression (x + y)n , we would have n + 1 term.
Use binomial theorem to expand expression (d - 1)4
The answer can be found using the Pascal’s triangle. For an expression , we would have n+ 1 term.
Use binomial theorem to expand expression (d - 1)4
The answer can be found using the Pascal’s triangle. For an expression , we would have n+ 1 term.
Use Pascal triangle to expand the expression (a - b)6 .
The answer can be found using the binomial expansion of
Use Pascal triangle to expand the expression (a - b)6 .
The answer can be found using the binomial expansion of
Use Pascal’s triangle to expand the expression (x + 1)5
The answer can be found using the binomial expansion of
Use Pascal’s triangle to expand the expression (x + 1)5
The answer can be found using the binomial expansion of
How many terms will there be in the expansion of the expression
. Explain how you know?
How many terms will there be in the expansion of the expression . Explain how you know?
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
has seven terms. Describe and correct
.what is the sum of the coefficients?
