Question
Use Pascal’s triangle to expand the expression (x + 1)5
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.
We are asked to find the expansion of the expression (x + 1)5 using Pascal’s triangle.
The correct answer is: n > 0
Step 1 of 2:
The given expression is (x + 1)5 . Here, the value of n=5. Thus, there would be 5+1=6 terms. Hence, we should use the sixth row of the Pascal’s triangle to write the corresponding expansion.
Step 2 of 2:
Analyzing the figure, we have:
Thus, the expansion is: 
.
Thus, the expansion is:
.The answer can be found using the binomial expansion of 
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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
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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
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the error the student may have made ?
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.what is the sum of the coefficients?
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. Justify your work.
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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.
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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
.
