Use binomial theorem to expand expression (x + y)⁷ .

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’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?

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.

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

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?

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.

Expand  using binomial theorem.

If an event has a probability of success p and a probability of failure q , then each term inthe expansion of(p+q)ⁿ represents a probability. For example , if a basketball player makes 60% of his free throw attempts , p= 0.6 and q= 0.4. To find the probability the basketball player will make exactly h out of k free throws, find  where  a coefficient of row k of Pascal’s triangle is, p is the probability of success, and q is the probability of failure.

Expand  using Pascal’s triangle.