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INSTRUCTION
Provide students with a piece of
graph paper to construct Pascal’s
Triangle.
Point out the symmetry in Pascal’s
Triangle. Show students that if
they were to fold the triangle
along its altitude, that the
numbers would match up.
Tell students that although
Pascal’s Triangle can be traced
back to China in the 12th century,
it was named for the French
Mathematician Blaise Pascal in the
17th century.
2. Substitute 3c for a, –4d for b, and 4 for n in the Binomial Theorem:
(3c – 4d) 4 = 4
C 0
(3c) 4 + 4
C 1
(3c) 3 (–4d) + 4
C 2
(3c) 2 (–4d) 2 + 4
C 3
(3c)(–4d) 3 +
4 C 4 (–4d)4 = 81c 4 – 432c 3 d + 864c 2 d 2 – 768cd 3 + 256d 4 .
3. Substitute 2p for a, 5q for b, and 6 for n in the general form of the 3rd
term of the binomial expansion: 6
C 2
(2p) 4 (5q) 2 = 400p 4 q 2 .
4. The expression 6
C 3
means “6 items chosen 3 at a time.”; it is evaluated
as
6!
.
3!( 6−
3)!
5. Multiply n by each of the positive integers less than it until you reach the
integer 1.
Think and Discuss
Answers
1. The coefficients of the terms
of the expansion are the
entries of a row of Pascal’s
Triangle.
9.5 The Binomial Theorem 417