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    • ▾Precalc
      • ▸Conic sections
        • •Intro to conic sections
        • •Center and radii of an ellipse
        • •Foci of an ellipse
        • •Intro to hyperbolas
        • •Foci of a hyperbola
        • •Maximizing the product of two integers, given their integer sum
        • •Hyperbolas not centered at the origin
        • •Standard equation of a circle
      • ▸Functions and relations
        • •Composition of functions
        • •Operations with functions
        • •Graphing the sum of trig functions from their graphs
        • •Finding and verifying the inverse of a nonlinear function
        • •Graphically finding the increasing, decreasing, and constant intervals
        • •Vertical and horizontal line tests
        • •Restrict the domain then find the inverse
        • •Sketching the inverse of a function from its graph
      • ▸Characteristics of functions
        • •Finding extrema graphically
        • •End behavior
      • ▸Rational functions
        • •Partial fraction decomposition
        • •Simplifying the difference quotient
        • •Pick's theorem
      • ▾Sigma notation and the binomial theorem
        • •Converting sums between sigma notation and expanded form
        • •Properties of sigma notation
        • •Using the binomial theorem
      • ▸Series
        • •Geometric series
        • •Geometric series with summation notation
        • •Arithmetic series with summation notation
      • ▸Logic
        • •De Morgan's laws for propositional logic
     › Precalc › Sigma notation and the binomial theorem

    Using the binomial theorem

    Students will learn what the binomial theorem is, and how to use it to expand binomials raised to whole number powers. After that, students will learn how to find specific terms for such expansions. This can be done by using the binomial theorem, without computing the entire expansion. For example, we can use the binomial theorem to pluck out the \(x^6\) term. Finally, students will learn the connection between the binomial theorem and Pascal's triangle. For a lesson, watch these: part 1, 2, 3, 4.

    Conclude by giving your students these challenges:

    • Consecutive Squares by NRICH
    • Do Unto Caesar by NRICH
    • Stretching Fractions by NRICH
    • 2015 AMC 8, Problem 2
    • Units of Big Powers

    Lessons and practice problems