Binomial Theorem
Essential Question: How can you use the
Binomial Theorem to expand a binomial?
Demonstrated in writing in summary at
the end of the notes.
BINOMIAL THEOREM
• For any positive integer n, the binomial
expansion of (a + b)n is:
(a + b)n = nC0anb0 + nC1an-1b1 + … + nCna0bn
• Notice that each term in the expansion of (a + b)n has
the form nCran-rbr where r is an integer from 0 to n.
Essential Question: How can you use the Binomial Theorem to expand a binomial?
Demonstrated in writing in summary at the end of the notes.
Example: Use the binomial theorem to
write the binomial expansion. (x + 4)3
Essential Question: How can you use the Binomial Theorem to expand a binomial?
Demonstrated in writing in summary at the end of the notes.
Example: Use the binomial theorem to write the
binomial expansion. (2m  n)4 = [2m + (____)]4
Essential Question: How can you use the Binomial Theorem to expand a binomial?
Demonstrated in writing in summary at the end of the notes.
Example: Find the coefficient of x5
in the expansion of (2x  7)9.
Essential Question: How can you use the Binomial Theorem to expand a binomial?
Demonstrated in writing in summary at the end of the notes.
Checkpoint Use the binomial theorem to write the binomial expansion.
• (a + 2b)3
• (6  s)4
• Find the coefficient of x8 in the expansion of (3x  2)10.
Essential Question: How can you use the Binomial Theorem to expand a binomial?
Demonstrated in writing in summary at the end of the notes.