Use polynomial identities to factor the polynomials or simplify the expressions :

How are Pascal’s triangle and binomial expansion such as (a + b)⁵ related?

You can find the expansion of (x + y)n  using both Pascal’s triangle and binomial expansion.

Use binomial theorem to expand .

Use polynomial identities to factor the polynomials or simplify the expressions :

Explain why the middle term  is 10x.

In the Binomial Expansion's middle term, in the expansion of (a + b)n, there are (n + 1) terms. Therefore, we can write the middle term or terms of (a + b)n based on the value of n. It follows that there will only be one middle term if n is even and two middle terms if n is odd.
The binomial expansions of (x + y)n are used to find specific terms, such as the term independent of x or y.
Practice Questions
1. Find the expansion of (9x - 2y)12's coefficient of x5y7.
2. In the expansion of (2x - y)11, locate the 8th term.

Use binomial theorem to expand  .

Use polynomial identities to factor the polynomials or simplify the expressions :

How can you use polynomial identities to rewrite expressions efficiently ?

Polynomial identities are equations that are true for all possible values of the variable and numbers.

Use binomial theorem to expand (2c + d)⁶

The expansion of the expression can also be found using the Pascal’s triangle. But, it is necessary to remember the values of the triangle to write down the expansion.

Use binomial theorem to expand  .

Use binomial theorem to expand (x - 1)⁷

For the expansion of an expression (x + y)n , we would have n+1 terms. This is something you need to keep in mind.

Use polynomial identities to factor the polynomials or simplify the expressions :

Use Pascal triangle to expand

Use binomial theorem to expand (s² + 3)⁵

For the expansion of an expression (x + y)n , we would have n+1 terms. This is something you need to keep in mind.

Use polynomial identities to factor the polynomials or simplify the expressions :

Use Pascal triangle to expand