Binomial theorem

The Binomial Theorem is a convenient way to multiply a binomial by itself. It can be applied to the powers of any binomials.

Basic concepts:
Combining the exponent rules
Combinations

Lessons

Notes:

- a)
  Pascal’s Triangle
- b)
  Binomial Theorem
2.
Expand:
3.
In the expansion of ${\left( {\frac{1}{{7{x^2}}} - {x^3}} \right)^{10}}$ , determine:

Binomial theorem

Don't just watch, practice makes perfect.

We have over 820 practice questions in Pre-Calculus for you to master.

Get Started Now

Try reviewing these fundamentals first

AlgebraCombining the exponent rules

StatisticsCombinations

Nope, got it.

Play next lesson

That's it, no more lessons

Practice this topic

Nope, got it.

Play next lesson

That's it, no more lessons

Goto next topic

Still don't get it?

Nope, I got it.

Still don't get it?

Review these basic concepts…

Combining the exponent rules

Combinations

Nope, I got it.

Play next lesson or Practice this topic

Start now and get better math marks!

Keep exploring StudyPug

Start now and get better math marks!

Keep exploring StudyPug

Lesson: 1

Selected

Lesson: 2a

Lesson: 2b

Lesson: 3a

Lesson: 3b

Lesson: 3c

Lesson: 4

Intro

Learn

Practice

Do better in math today

Don't just watch, practice makes perfect.

Do better in math today

Don't just watch, practice makes perfect.

Lessons

Notes:

1.

Expand (a+b)4{\left( {a + b} \right)^4}(a+b)​4​​, using:

a)

Pascal’s Triangle

b)

Binomial Theorem

2.

Expand:

a)

(5x+2)3{\left( {5x + 2} \right)^3}(5x+2)​3​​

b)

(2x−3y)4{\left( {2x - 3y} \right)^4}(2x−3y)​4​​

3.

In the expansion of (17x2−x3)10{\left( {\frac{1}{{7{x^2}}} - {x^3}} \right)^{10}}(​7x​2​​​​1​​−x​3​​)​10​​ , determine:

a)

the 4th term

b)

the middle term

c)

the constant term

4.

In the expansion of (3−2x)8{\left( {3 - 2x} \right)^8}(3−2x)​8​​ , determine the coefficient of the term containing X5{X^5}X​5​​.

Don't just watch, practice makes perfect.

Binomial theorem

Don't just watch, practice makes perfect.

We have over 820 practice questions in Pre-Calculus for you to master.

Algebra
Combining the exponent rules

Statistics
Combinations

or

Expand ${\left( {a + b} \right)^4}$ , using:

${\left( {5x + 2} \right)^3}$

${\left( {2x - 3y} \right)^4}$

In the expansion of ${\left( {\frac{1}{{7{x^2}}} - {x^3}} \right)^{10}}$ , determine:

In the expansion of ${\left( {3 - 2x} \right)^8}$ , determine the coefficient of the term containing ${X^5}$ .