Binomial theorem

Binomial theorem

The Binomial Theorem is another method to help us expand binomials in a faster manner. It is particularly useful when we work on binomial expansions that involve binomials raised to high powers.
Basic concepts: Combining the exponent rules, Combinations,

Lessons


binomial theorem
  • 1.
    Expand (a+b)4{\left( {a + b} \right)^4}, using:
    a)
    Pascal’s Triangle

    b)
    Binomial Theorem

  • 2.
    Expand:
    a)
    (5x+2)3{\left( {5x + 2} \right)^3}

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

  • 3.
    In the expansion of (17x2−x3)10{\left( {\frac{1}{{7{x^2}}} - {x^3}} \right)^{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} , determine the coefficient of the term containing X5{X^5}.
Do better in math today
Get Started Now
2.
Polynomials
2.1
Polynomial long division
2.2
Polynomial synthetic division
2.3
Determining the equation of a polynomial function
2.4
Factor theorem
2.5
Rational zero theorem
2.6
Characteristics of polynomial graphs
2.7
Multiplicities of polynomials
2.8
Imaginary zeros of polynomials
2.9
Pascal's triangle
2.10
Binomial theorem
2.11
What is a polynomial function?
2.12
Applications of polynomial functions
2.13
Solving polynomial inequalities
2.14
Descartes’ rule of signs
Precalculus
Don't just watch, practice makes perfect.