MA19.PRE.17

Mathematics (2019) Grade(s): 09-12 - Precalculus

MA19.PRE.17
Know and apply the Binomial Theorem for the expansion of $(x + y)^n$ in powers of x and y for a positive integer, n, where x and y are any numbers.

Unpacked Content

Knowledge

Students know:

Distributive Property of multiplication over addition for polynomials.
The generation pattern for Pascal's Triangle and which binomial expansion term has coefficients corresponding to each row.
Simplification procedures for expressions involving the number of combinations of n things taken r at a time.
The patterns of coefficients and exponents in a binomial expansion.

Skills

Students are able to:

Accurately perform algebraic manipulations on polynomial expressions.
Generate rows of Pascal's Triangle.
Accurately perform simplification procedures for expressions involving the number of combinations of n things taken r at a time.
Apply the patterns of coefficients and exponents to expand any binomial raised to a power.

Understanding

Students understand that:

Regularities noted in one part of mathematics may also be seen in very different areas of mathematics, (i.e., Pascal's Triangle from counting procedures and the Binomial Theorem). These regularities are useful in computing or manipulating mathematical expressions.
The regularities that are seen in exponents and coefficients in a binomial expansion will be generalized to all binomials to aid in identifying specific terms.

Vocabulary

Binomial Theorem
Pascal's Triangle
Combinatorial Argument
Mathematical induction

Aligned Learning Resources

Binomial Expansion -Shortcut Please

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